Descriptor: "set inversion" / Topic: 02 engineering and technology - Searchworks@Jio Institute Digital Library Search Results

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43 results on '"set inversion"'

1. Robust Interval Luenberger Observer-Based State Feedback Control: Application to a Multi-DOF Micropositioner

Author: Philippe Lutz, Abdenbi Mohand-Ousaid, Mounir Hammouche, Micky Rakotondrabe, Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174) (FEMTO-ST), Université de Technologie de Belfort-Montbeliard (UTBM)-Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM)-Université de Franche-Comté (UFC), and Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS) more...
Subjects: 0209 industrial biotechnology, Set inversion, Computer science, Computation, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], 020208 electrical & electronic engineering, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Interval arithmetic, 020901 industrial engineering & automation, Control and Systems Engineering, Robustness (computer science), Control theory, 0202 electrical engineering, electronic engineering, information engineering, Symmetric matrix, State observer, Electrical and Electronic Engineering, Robust control, Eigenvalues and eigenvectors
Abstract: International audience; Controlling multi-DOF (Degree of Freedom) micropositioning systems always represents great challenge becauseof the high sensitivity to the environment at this scale and the cross-coupling effects present between the different axes. A robust Luenberger observer-based state feedback design using interval analysis and regional pole assignment technique are introduced to control such systems. This robust control design keeps the same structure of the classical state-feedback with the usual Luenberger observer. However, the synthesises of the observer and the feedback controller are performed by means of interval techniques to find the set of gains that are robustagainst system uncertainties and that satisfy some predefined performances. For this matter, an algorithm based on Set Inversion Via Interval Analysis (SIVIA) combined with interval eigenvalues computation is proposed to find these robust gains. The control approach is validated in simulation and then tested experimentally to control a multi-DOF positioning structure. more...
Published: 2019
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2. Guaranteed Identification of Viscous Friction for a Nonlinear Inverted Pendulum Through Interval Analysis and Set Inversion

Author: Alexandre dit Sandretto, Julien, Fnadi, Mohamed, Dit Sandretto, Julien Alexandre, Ballet, Gabriel, Pribourg, Laurent, Unité d'Informatique et d'Ingénierie des Systèmes (U2IS), and École Nationale Supérieure de Techniques Avancées (ENSTA Paris) more...
Subjects: 0209 industrial biotechnology, Interval vector, Inertial frame of reference, Set inversion, Computer science, 020208 electrical & electronic engineering, Ode, 02 engineering and technology, Domain (mathematical analysis), Interval arithmetic, Inverted pendulum, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear system, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, ComputingMilieux_MISCELLANEOUS
Abstract: This paper focuses on the guaranteed identification of viscous friction parameters for a nonlinear inverted pendulum. The method is based on the interval analysis (IA) and set-inversion tools to determine the set of all the feasible friction parameters from a prior domain of interest, i.e. initial interval vector or box, that are consistent with all the experimental and theoretical datasets including their uncertainties. The capabilities of our proposed guaranteed identification are compared with the more commonly used approach based on the least square method identification (LSMI), which is used especially to adjust the inertial and geometric parameters of our experimental plant. Both of them have been investigated through several experiments on a real inverted pendulum and simulations with uncertain ODEs via the DynIbex library. more...
Published: 2021
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3. A boundary approach for set inversion

Author: Luc Jaulin, Equipe ROBotics for EXploration (Lab-STICC_ROBEX), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne) more...
Subjects: 0209 industrial biotechnology, Artificial intelligence, Set inversion, Computer science, Continuous domains, Boundary, Mathematical analysis, Boundary (topology), 02 engineering and technology, Interval (mathematics), Constraint propagation, Inversion (discrete mathematics), Domain (mathematical analysis), Image (mathematics), [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Set (abstract data type), 020901 industrial engineering & automation, Control and Systems Engineering, Set Inversion, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Interval analysis, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, Volume (compression)
Abstract: In the paper, we present a new interval-based set inversion algorithm which takes into account the continuity of the problem. In the case where the set Y to be inverted has some volume, we show that inverting the boundary ∂ Y of Y is sufficient to reconstruct the preimage X = f − 1 ( Y ) . The inversion of ∂ Y separates the domain of f into two regions : one inside X and one outside. To detect which part is inside or outside, we show that we can retro-propagate the information coming from Y at negligible cost. The efficiency of the approach is illustrated on a localization problem. more...
Published: 2021
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4. Robust and guaranteed output-feedback force control of piezoelectric actuator under temperature variation and input constraints

Author: Mounir Hammouche, Philippe Lutz, Micky Rakotondrabe, Centre National de la Recherche Scientifique - CNRS (FRANCE), Ecole Nationale Supérieure de Mécanique et des Microtechniques - ENSMM (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université de Franche-Comté (FRANCE), Université de Technologie de Belfort-Montbéliard - UTBM (FRANCE), Université Bourgogne Franche-Comté - UBFC (FRANCE), Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174) (FEMTO-ST), Université de Technologie de Belfort-Montbeliard (UTBM)-Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Génie de Production (LGP), and Ecole Nationale d'Ingénieurs de Tarbes more...
Subjects: Input constraint, 0209 industrial biotechnology, Set inversion, Computer science, Robust output-feedback, Computation, Interval models, 02 engineering and technology, Interval (mathematics), Sense (electronics), Set inversionvia interval analysis, Piezoelectric tube actuator, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), 020901 industrial engineering & automation, Amplitude, Control and Systems Engineering, Control theory, Bounded function, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Robotique, Eigenvalues and eigenvectors
Abstract: International audience; This paper addresses the control of manipulation force in a piezoelectric tubeactuator (piezotube) subjected to temperature variation and input constrains.To handle this problem a robust output-feedback design is proposed using aninterval state-space model, which permits consideration of the parameter uncertainties caused by temperature variation. The design method is robust in the sense that the eigenvalues of the interval system are designed to be clustered inside desired regions. For that, an algorithm based on Set Inversion Via IntervalAnalysis (SIVIA) combined with interval eigenvalues computation is proposed. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions of the feedback gain[K]that satisfy the inclusion of the eigenvalues of the closed-loop system in the desired region, while at the same time ensuring the control inputs amplitude is bounded by specified saturation. The effectiveness of the control strategy is illustrated by experiments on a real piezotube of which the environmental temperature is varied. more...
Published: 2020
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5. Dynamic identification of axial force and boundary restraints in tie rods and cables with uncertainty quantification using Set Inversion Via Interval Analysis

Author: Ehab Al-Shaer, Timothy P. Kernicky, and Matthew J. Whelan
Subjects: Acoustics and Ultrasonics, Set inversion, business.industry, Computer science, Mechanical Engineering, Structural system, Natural frequency, 02 engineering and technology, Structural engineering, Condensed Matter Physics, 01 natural sciences, Parameter identification problem, 020303 mechanical engineering & transports, 0203 mechanical engineering, Mechanics of Materials, 0103 physical sciences, Measurement uncertainty, Structural health monitoring, Boundary value problem, Uncertainty quantification, business, 010301 acoustics
Abstract: A methodology is developed for the estimation of internal axial force and boundary restraints within in-service, prismatic axial force members of structural systems using interval arithmetic and contractor programming. The determination of the internal axial force and end restraints in tie rods and cables using vibration-based methods has been a long standing problem in the area of structural health monitoring and performance assessment. However, for structural members with low slenderness where the dynamics are significantly affected by the boundary conditions, few existing approaches allow for simultaneous identification of internal axial force and end restraints and none permit for quantifying the uncertainties in the parameter estimates due to measurement uncertainties. This paper proposes a new technique for approaching this challenging inverse problem that leverages the Set Inversion Via Interval Analysis algorithm to solve for the unknown axial forces and end restraints using natural frequency measurements. The framework developed offers the ability to completely enclose the feasible solutions to the parameter identification problem, given specified measurement uncertainties for the natural frequencies. This ability to propagate measurement uncertainty into the parameter space is critical towards quantifying the confidence in the individual parameter estimates to inform decision-making within structural health diagnosis and prognostication applications. The methodology is first verified with simulated data for a case with unknown rotational end restraints and then extended to a case with unknown translational and rotational end restraints. A laboratory experiment is then presented to demonstrate the application of the methodology to an axially loaded rod with progressively increased end restraint at one end. more...
Published: 2018
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6. Chain of Set Inversion Problems Application to reachability analysis

Author: Luc Jaulin, Benoit Desrochers, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL) more...
Subjects: Large class, Discrete mathematics, 0209 industrial biotechnology, State system, Set inversion, Solution set, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Chain (algebraic topology), Control and Systems Engineering, Reachability, 0101 mathematics, Mathematics
Abstract: International audience; This paper deals with the set inversion problem X = f −1 (Y) in the case where f : R n → R m depends on a parameter vector p ∈ R q which is known to be inside a box [p]. We show that for a large class of problems, we can obtain an accurate approximation of the solution set, without bisecting in the p-space. To do this, symbolic methods are required to cast our initial problem into a chain of set-inversion problems, the links of which have some nice properties with respect to p. As an application, we consider the problem of computing the set of all initial states of an uncertain discrete-time state system that reach a target set Y in a given time. more...
Published: 2017
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7. Guaranteed Nonlinear Parameter Estimation with Additive Gaussian Noise

Author: Jeremy Nicola, Luc Jaulin, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Olga Kosheleva, Sergey P. Shary, Gang Xiang, Roman Zapatrin, and Janusz Kacprzyk more...
Subjects: 0209 industrial biotechnology, Set inversion, Estimation theory, Set-estimation, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Nonlinear parameter estimation, 02 engineering and technology, Interval arithmetic, Set (abstract data type), Probabilistic estimation, [SPI]Engineering Sciences [physics], symbols.namesake, 020901 industrial engineering & automation, Gaussian noise, Localization, Parameter estimation, 0202 electrical engineering, electronic engineering, information engineering, symbols, Interval analysis, Applied mathematics, 020201 artificial intelligence & image processing, Set estimation, Mathematics
Abstract: International audience; In this paper we propose a new approach for nonlinear parameter estimation under additive Gaussian noise. We provide an algorithm based on interval analysis and set inversion which computes an inner and an outer approximation of a set enclosing the parameter vector with a given probability. The principle of the approach is illustrated by examples related to parameter estimation and range-only localization. more...
Published: 2020
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8. Dynamic Set-Inversion Procedure to Design Interval-Based State Estimators for Discrete-Time LPV Systems

Author: Sören Hohmann, Nacim Meslem, Stefan Krebs, Karlsruher Institut für Technologie (KIT), GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and Meslem, Nacim more...
Subjects: 0209 industrial biotechnology, Sequence, Set inversion, [SPI] Engineering Sciences [physics], Estimator, 02 engineering and technology, Interval (mathematics), Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, [SPI]Engineering Sciences [physics], [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Discrete time and continuous time, Bounded function, Applied mathematics, A priori and a posteriori, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: This publication is devoted to the design of an interval-based set-membership state estimator that can be applied to totally observable linear parameter-varying (LPV) systems. Hereto, a set-inversion procedure to determine state intervals that are consistent with a sequence of input and output values as well as two intersections with predicted values are used to reduce the pessimism of interval arithmetic. A numerical example illustrating the performance of the method is presented. The benefit of this method is that it provides an a priori known accuracy of the result based on the assumption of unknown but bounded uncertainties. more...
Published: 2019

9. Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System

Author: Luc Jaulin, Andreas Rauh, Swantje Romig, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Department of Mechatronics, and University of Rostock more...
Subjects: 0209 industrial biotechnology, Numerical Analysis, Set inversion, Sliding mode control, Computer science, 02 engineering and technology, Interval (mathematics), Invariant sets, Theoretical Computer Science, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computational Mathematics, Nonlinear system, 020901 industrial engineering & automation, Computational Theory and Mathematics, Bounded function, Lyapunov stability, 0202 electrical engineering, electronic engineering, information engineering, Interval analysis, 020201 artificial intelligence & image processing, Invariant (mathematics), Global optimization, Algorithm
Abstract: In recent years, many applications, as well as theoretical properties of interval analysis have been investigated. Without any claim for completeness, such applications and methodologies range from enclosing the effect of round-off errors in highly accurate numerical computations over simulating guaranteed enclosures of all reachable states of a dynamic system model with bounded uncertainty in parameters and initial conditions, to the solution of global optimization tasks. By exploiting the fundamental enclosure properties of interval analysis, this paper aims at computing invariant sets of nonlinear closed-loop control systems. For that purpose, Lyapunov-like functions and interval analysis are combined in a novel manner. To demonstrate the proposed techniques for enclosing invariant sets, the systems examined in this paper are controlled via sliding mode techniques with subsequently enclosing the invariant sets by an interval based set inversion technique. The applied methods for the control synthesis make use of a suitably chosen Gr&ouml, bner basis, which is employed to solve B&eacute, zout&rsquo, s identity. Illustrating simulation results conclude this paper to visualize the novel combination of sliding mode control with an interval based computation of invariant sets. more...
Published: 2019
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10. Ellipsoidal Set Membership Filtering with Reduced Conservatism Applied to Relative Localization Between Aircraft Based on GNSS and UWB Ranging

Author: S. Fergani and Jan Bolting
Subjects: 0209 industrial biotechnology, Set inversion, Computer science, 020208 electrical & electronic engineering, Ranging, 02 engineering and technology, Filter (signal processing), Reduction (complexity), Set (abstract data type), 020901 industrial engineering & automation, GNSS applications, 0202 electrical engineering, electronic engineering, information engineering, Benchmark (computing), Algorithm, Parametric statistics
Abstract: For automatic formation flight and applications such as automatic aerial refueling, relative positions between aircraft need to be accurately estimated. However, to ensure flight safety, guaranteed consistent uncertainty estimates are of equally crucial importance. This paper presents a novel Iterated Extended Set Membership Filter (IESMF) providing ellipsoidal regions guaranteed to contain another aircraft's position in a formation. Two easily implementable modifications to the Extended Set Membership Filter are shown to greatly reduce its conservatism. The filter runs in fixed time and handles asynchronous observations. As another novelty, we take into account parametric uncertainty of the observation equation. The proposed filter is applied to a realistic UAS localization benchmark simulation. We compare the new filter to a computationally very strong but much more expensive nonlinear set inversion algorithm and find that similar performances can be achieved. Also, simulation results illustrate the effective reduction of filter conservatism by a few iterative updates. more...
Published: 2019
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11. Interval Superposition Arithmetic for Guaranteed Parameter Estimation

Author: Yanlin Zha, Kai Wang, Boris Houska, Mario E. Villanueva, Junyan Su, and Radoslav Paulen
Subjects: 0209 industrial biotechnology, Set inversion, Computer science, Estimation theory, 020208 electrical & electronic engineering, Context (language use), Numerical Analysis (math.NA), 02 engineering and technology, Interval (mathematics), Image (mathematics), Set (abstract data type), Reduction (complexity), Superposition principle, 020901 industrial engineering & automation, Control and Systems Engineering, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Mathematics - Numerical Analysis, Arithmetic
Abstract: The problem of guaranteed parameter estimation (GPE) consists in enclosing the set of all possible parameter values, such that the model predictions match the corresponding measurements within prescribed error bounds. One of the bottlenecks in GPE algorithms, commonly exploiting set inversion, is the construction of enclosures for the image-set of factorable functions. In this paper, we introduce a novel set-based computing method called interval superposition arithmetics (ISA) for the construction of enclosures of such image sets and its use in GPE algorithms. The main benefits of using ISA in the context of GPE lie in the improvement of enclosure accuracy and in the implied reduction of the number of set-membership tests in the set-inversion algorithm. more...
Published: 2019
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12. Cooperative Localization of Drones by using Interval Methods

Author: Vincent Drevelle, Ide Flore Kenmogne, Eric Marchand, Sensor-based and interactive robotics (RAINBOW), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE (IRISA-D5), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Sensor-based and interactive robotics ( RAINBOW ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE ( IRISA_D5 ), Institut de Recherche en Informatique et Systèmes Aléatoires ( IRISA ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Institut National des Sciences Appliquées - Rennes ( INSA Rennes ) -Université de Bretagne Sud ( UBS ) -École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -CentraleSupélec-Centre National de la Recherche Scientifique ( CNRS ) -IMT Atlantique Bretagne-Pays de la Loire ( IMT Atlantique ) -Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Institut National des Sciences Appliquées - Rennes ( INSA Rennes ) -Université de Bretagne Sud ( UBS ) -École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -CentraleSupélec-Centre National de la Recherche Scientifique ( CNRS ) -IMT Atlantique Bretagne-Pays de la Loire ( IMT Atlantique ) -Institut de Recherche en Informatique et Systèmes Aléatoires ( IRISA ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Institut National des Sciences Appliquées - Rennes ( INSA Rennes ) -Université de Bretagne Sud ( UBS ) -École normale supérieure - Rennes ( ENS Rennes ) -CentraleSupélec-Centre National de la Recherche Scientifique ( CNRS ) -IMT Atlantique Bretagne-Pays de la Loire ( IMT Atlantique ), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes 1 (UR1), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique) more...
Subjects: 0209 industrial biotechnology, vision, Information Systems and Management, Computer science, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Context (language use), ComputerApplications_COMPUTERSINOTHERSYSTEMS, 02 engineering and technology, Management Science and Operations Research, Theoretical Computer Science, Interval arithmetic, 020901 industrial engineering & automation, Position (vector), intervals, 0202 electrical engineering, electronic engineering, information engineering, Computer Science (miscellaneous), [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Computer vision, Electrical and Electronic Engineering, Pose, ComputingMilieux_MISCELLANEOUS, Set inversion, constraint propaga- tion, business.industry, [ INFO.INFO-RB ] Computer Science [cs]/Robotics [cs.RO], cooperative localization, Ranging, Local consistency, Robot, 020201 artificial intelligence & image processing, Computer Vision and Pattern Recognition, Artificial intelligence, business, Software
Abstract: In this article we address the problem of cooperative pose estimation in a group of unmanned aerial vehicles (UAVs) in a bounded-error context. The UAVs are equipped with cameras to track landmarks, and with a communication and ranging system to cooperate with their neighbors. Measurements are represented by intervals, and constraints are expressed on the robots poses (positions and orientations). Pose domains subpavings are obtained by using set inversion via interval analysis. Each robot of the group first computes a pose domain using only its sensors measurements. Then, through position boxes exchanges, the positions are cooperatively refined by constraint propagation in the group. Results with real robot data are presented, and show that the position accuracy is improved thanks to cooperation. more...
Published: 2019

13. Using constraint propagation for cooperative UAV localization from vision and ranging

Author: Ide-Flore Kenmogne, Eric Marchand, Vincent Drevelle, Sensor-based and interactive robotics (RAINBOW), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE (IRISA-D5), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Sensor-based and interactive robotics ( RAINBOW ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE ( IRISA_D5 ), Institut de Recherche en Informatique et Systèmes Aléatoires ( IRISA ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Institut National des Sciences Appliquées - Rennes ( INSA Rennes ) -Université de Bretagne Sud ( UBS ) -École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -CentraleSupélec-Centre National de la Recherche Scientifique ( CNRS ) -IMT Atlantique Bretagne-Pays de la Loire ( IMT Atlantique ) -Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Institut National des Sciences Appliquées - Rennes ( INSA Rennes ) -Université de Bretagne Sud ( UBS ) -École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -CentraleSupélec-Centre National de la Recherche Scientifique ( CNRS ) -IMT Atlantique Bretagne-Pays de la Loire ( IMT Atlantique ) -Institut de Recherche en Informatique et Systèmes Aléatoires ( IRISA ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Institut National des Sciences Appliquées - Rennes ( INSA Rennes ) -Université de Bretagne Sud ( UBS ) -École normale supérieure - Rennes ( ENS Rennes ) -CentraleSupélec-Centre National de la Recherche Scientifique ( CNRS ) -IMT Atlantique Bretagne-Pays de la Loire ( IMT Atlantique ), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Bretagne Sud (UBS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1) more...
Subjects: 0209 industrial biotechnology, Set inversion, Computer science, business.industry, Constraints propagation, [ INFO.INFO-RB ] Computer Science [cs]/Robotics [cs.RO], Intervals, Cooperative localization, 020207 software engineering, Context (language use), Ranging, 02 engineering and technology, Interval arithmetic, Domain (software engineering), 020901 industrial engineering & automation, Position (vector), 0202 electrical engineering, electronic engineering, information engineering, Local consistency, Robot, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Computer vision, Artificial intelligence, business
Abstract: International audience; This paper addresses the problem of cooperative localization in a group of unmanned aerial vehicles (UAV) in a bounded error context. The UAVs are equipped with cameras to tracks landmarks, and a communication and ranging system to cooperate with their neighbours. Measurements are represented by intervals, and constraints are expressed on the robots poses (positions and orientations). Each robot first computes a pose domain using only its sensors measurements, by using set inversion via interval analysis [1]. Then, through position boxes exchange, positions are cooperatively refined by constraint propagation in the group. Results are presented with real robot data, and show position accuracy improvement thanks to cooperation. more...
Published: 2018
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14. Validated Enclosure of Uncertain Nonlinear Equations Using SIVIA Monte Carlo

Author: Nisha Rani Mahato, Snehashish Chakraverty, Jean Dezert, Luc Jaulin, National Institute of Technology Rourkela, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), DTIS, ONERA, Université Paris Saclay (COmUE) [Palaiseau], and ONERA-Université Paris Saclay (COmUE) more...
Subjects: Van der Pol oscillator, Dynamical systems theory, Set inversion, Differential equation, Monte Carlo method, 020206 networking & telecommunications, 02 engineering and technology, Interval (mathematics), SIVIA Monte Carlo, Nonlinear oscillator, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear system, [SPI]Engineering Sciences [physics], 020303 mechanical engineering & transports, Uncertain nonlinear equations, 0203 mechanical engineering, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Dependency problem, Contractor, Mathematics
Abstract: International audience; The dynamical systems in various science and engineering problems are often governed by nonlinear equations (differential equations). Due to insufficiency and incompleteness of system information, the parameters in such equations may have uncertainty. Interval analysis serves as an efficient tool for handling uncertainties in terms of closed intervals. One of the major problems with interval analysis is handling “dependency problems” for computation of the tightest range of solution enclosure or exact enclosure. Such dependency problems are often observed while dealing with complex nonlinear equations. In this regard, initially, two test problems comprising interval nonlinear equations are considered. The Set Inversion via Interval Analysis (SIVIA) along with the Monte Carlo approach is used to compute the exact enclosure of the test problems. Further, the efficiency of the proposed approach has also been verified for solving nonlinear differential equation (Van der Pol oscillator) subject to interval initial conditions. more...
Published: 2018
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15. Inversion Fractals and Iteration Processes in the Generation of Aesthetic Patterns

Author: Krzysztof Gdawiec
Subjects: Set inversion, Computer science, Chaos game, Fixed-point theorem, 020207 software engineering, 02 engineering and technology, Computer Graphics and Computer-Aided Design, Inversion (discrete mathematics), Fractal, Iterated function, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Algorithm, ComputingMethodologies_COMPUTERGRAPHICS
Abstract: In this paper, we generalize the idea of star-shaped set inversion fractals using iterations known from fixed point theory. We also extend the iterations from real parameters to so-called q-system numbers and proposed the use of switching processes. All the proposed generalizations allowed us to obtain new and diverse fractal patterns that can be used, e.g. as textile and ceramics patterns. Moreover, we show that in the chaos game for iterated function systems-which is similar to the inversion fractals generation algorithm-the proposed generalizations do not give interesting results. more...
Published: 2015
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16. Robust set-membership parameter estimation of the glucose minimal model

Author: Pau Herrero, Christofer Toumazou, Benoît Delaunay, Nick Oliver, Luc Jaulin, and Pantelis Georgiou
Subjects: 0209 industrial biotechnology, Computational complexity theory, Set inversion, Estimation theory, Computer science, 030209 endocrinology & metabolism, 02 engineering and technology, Fault detection and isolation, Interval arithmetic, Minimal model, Set (abstract data type), 03 medical and health sciences, 020901 industrial engineering & automation, 0302 clinical medicine, Control and Systems Engineering, Robustness (computer science), Signal Processing, Electrical and Electronic Engineering, Algorithm
Abstract: The minimal model of glucose-insulin dynamics is currently being used in several diabetes-related applications, such as investigating the glucose metabolism, and in the developments of model predictive controllers and fault detection techniques for automatic blood glucose control i.e., artificial pancreas. Different approaches have been proposed to identify this model, but none of them is capable of providing guaranteed robust enclosures for its parameters, something very desired in applications such as the artificial pancreas, where robustness is paramount. This paper presents a novel approach for guaranteed set-membership parameter estimation of the minimal model based on the well-renowned Set Inversion via Interval Analysis SIVIA algorithm. Because the computational complexity of this algorithm is the main barrier for its applicability, an efficient vectorial implementation of SIVIA was employed. Clinical data from a standard intravenous glucose tolerance test were used to prove the validity of the presented approach. Finally, Modal Interval Analysis was used to reduce the numerical overestimation due to the dependency problem of interval arithmetic and significantly speeding up the computations. Copyright © 2015 John Wiley & Sons, Ltd. more...
Published: 2015
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17. Thick set inversion

Author: Benoit Desrochers, Luc Jaulin, Délégation générale de l'armement (DGA), Ministère de la Défense, Lab-STICC_ENSTAB_CID_PRASYS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL), Pôle STIC_OSM, École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT) more...
Subjects: Discrete mathematics, Linguistics and Language, Set inversion, Efficient algorithm, Uncertainty, 010103 numerical & computational mathematics, 02 engineering and technology, Function (mathematics), 01 natural sciences, Language and Linguistics, Interval arithmetic, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Set (abstract data type), Artificial Intelligence, Set function, Index set, 0202 electrical engineering, electronic engineering, information engineering, Constraint programming, Set-Membership methods, 020201 artificial intelligence & image processing, 0101 mathematics, Interval Analysis, Mathematics
Abstract: This paper deals with the set inversion problem X = f − 1 ( Y ) in the case where the function f : R n → R m and the set Y are both uncertain. The uncertainty is treated under the form of intervals. More precisely, for all x, f ( x ) is inside the box [ f ] ( x ) and the uncertain set Y is bracketed between an inner set Y ⊂ and an outer set Y ⊃ . The introduction of new tools such as thick intervals and thick boxes will allow us to propose an efficient algorithm that handles the uncertainty of sets in an elegant and efficient manner. Some elementary test-cases that cannot be handled easily and properly by existing methods show the efficiency of the approach. more...
Published: 2017
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18. An active learning framework for set inversion

Author: Vu Dinh, Duy M. H. Nguyen, Lam Si Tung Ho, and Binh T. Nguyen
Subjects: Information Systems and Management, Set inversion, Computer science, Active learning (machine learning), 02 engineering and technology, Management Information Systems, Interval arithmetic, Set (abstract data type), Data point, Artificial Intelligence, Control theory, 020204 information systems, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Algorithm, Software
Abstract: Set inversion is a classical problem in control theory that has many important applications in various fields of science and engineering. The state-of-the-art method for solving this problem, Set Inverter Via Interval Analysis (SIVIA), usually does not work well in high dimensions and often fails to recover sets with complicated structures. In this work, we propose a new approach to the problem of set inversion, which employs techniques from machine learning to resolve these issues. Our algorithm can handle problems in high dimensions and achieve the same level of accuracy with fewer data points compared to SIVIA. We illustrate the performance of our method in various simulation studies and apply it to investigate the dynamics of the 17th-century plague in Eyam village, England. more...
Published: 2019
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19. Localization Confidence Domains via Set Inversion on Short-Term Trajectory

Author: Vincent Drevelle, Philippe Bonnifait, Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), and Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS) more...
Subjects: 0209 industrial biotechnology, Computer science, 02 engineering and technology, Precise Point Positioning, localization, Interval arithmetic, 020901 industrial engineering & automation, 0502 economics and business, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Computer vision, Electrical and Electronic Engineering, sensor fusion, 050210 logistics & transportation, Ground truth, Set inversion, business.industry, 05 social sciences, Sensor fusion, Computer Science Applications, Control and Systems Engineering, 3-D map, Local consistency, Global Positioning System, Artificial intelligence, Global Positioning System (GPS), business, Particle filter
Abstract: International audience; The knowledge of localization uncertainties is of prime importance when the navigation of intelligent vehicles has to deal with safety issues. This paper presents a robust estimation method that is able to quantify the localization confidence based on interval analysis and constraint propagation. First, tightly coupled position domains are computed by constraint propagation on Global Positioning System (GPS) measurements and a precise 3-D map of the drivable area. Since GPS is prone to satellite masking and wrong measurements in urban areas, a second stage provides localization integrity and information availability by the use of a position and proprioceptive data history. A robust constraint propagation algorithm is employed to compute the current vehicle pose. It is able to handle erroneous positions with a chosen integrity risk. Experiments carried out in urban canyons illustrate the performance of the method in comparison with a particle filter. Despite bad satellite visibility, full positioning availability is obtained, and errors are less than 5.1 m during 95% of the trial. In opposition to the particle filter, confidence domains are consistent with ground truth, which confirms the high integrity of the method. more...
Published: 2013
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20. Cooperative Localization with Reliable Confidence Domains between Vehicles sharing GNSS Pseudoranges Errors with no Base Station

Author: Philippe Bonnifait, Khaoula Lassoued, Isabelle Fantoni, Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire d'Excellence 'Maîtrise des Systèmes de Systèmes Technologiques' (Labex MS2T) more...
Subjects: 050210 logistics & transportation, 0209 industrial biotechnology, GNSS augmentation, Set inversion, Computer science, Mechanical Engineering, 05 social sciences, Pseudorange, Control engineering, 02 engineering and technology, Sensor fusion, Computer Science Applications, 020901 industrial engineering & automation, GNSS applications, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0502 economics and business, Automotive Engineering, Dead reckoning, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Observability, Air navigation, Algorithm
Abstract: International audience; Cooperation between road vehicles through information exchange is a promising way to enhance their absolute and relative positions. This paper presents an approach for generating, sharing and applying Global Navigation Satellite System (GNSS) pseudorange corrections through a V2X communication network. Conventionally, differential corrections are generated by fixed base stations with known positions and sent to mobile users. Here, the proposed cooperative method has no central server and the estimation of the raw measurements errors is done in a fully distributed way. Using a model of the correlation of the pseudorange errors and through the knowledge of the local motions of the vehicles obtained by Dead Reckoning (DR) or tracking, a non linear observability shows that the estimation problem is solvable. A cooperative and fully distributed estimation method is then presented using Set Inversion and Constraint propagation techniques. Positions, pseudorange estimated errors and DR data are shared in the network of vehicles and confidence is handled by intervals, in a bounded error context. This allows computing highly reliable confidence domains with no direct range measurements, which is crucial for applications involving close proximity navigation. Indeed, the proposed data fusion framework does not require any linearization of the equations and is insensitive to the data incest problem since the same information can be exploited several times in the computation process without making the estimation over-converge. Results using real measurements are presented to illustrate the performance of the proposed cooperative method in comparison with standalone estimation. A classical sequential Bayesian method has also been implemented on the same data set and compared in terms of accuracy and confidence with a ground truth system. more...
Published: 2017
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21. Cooperative localization of vehicles sharing GNSS pseudoranges corrections with no base station using set inversion

Author: Philippe Bonnifait, Khaoula Lassoued, Isabelle Fantoni, Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire d'Excellence 'Maîtrise des Systèmes de Systèmes Technologiques' (Labex MS2T) more...
Subjects: 0209 industrial biotechnology, Set inversion, Computer science, 020208 electrical & electronic engineering, Control engineering, 02 engineering and technology, Ephemeris, Radio propagation, Base station, 020901 industrial engineering & automation, GNSS applications, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Algorithm
Abstract: International audience; Fully distributed localization methods with no central server are relevant for autonomous vehicles that need real-time cooperation. In this paper, mobile vehicles share estimates of GNSS pseudoranges common errors also known as biases. The biases that affect the pseudoranges are mainly due to signal propagation and inaccurate ephemeris data. By describing the measurements models as geometric constraints on intervals, cooperative localization turns into distributed set inversion problem. The solution of this problem is guaranteed to contain the true vehicles positions. We consider vehicles which cooperate and exchange information in order to improve the absolute and relative estimation by fusing pseudoranges corrections shared between them. Results using real measurements are presented to illustrate the performance of the proposed approach in comparison with a standalone method. more...
Published: 2016
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22. Design of a Fixed-Order RST Controller for Interval Systems: Application to the Control of Piezoelectric Actuators

Author: Sofiane Khadraoui, Micky Rakotondrabe, and Philippe Lutz
Subjects: 0209 industrial biotechnology, Engineering, Set inversion, business.industry, Computation, 020208 electrical & electronic engineering, Open-loop controller, Control engineering, 02 engineering and technology, Interval arithmetic, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Robustness (computer science), Bounded function, 0202 electrical engineering, electronic engineering, information engineering, Piezoelectric actuators, business, Parametric statistics
Abstract: This paper presents a technique for designing a robust polynomial RST controller for parametric uncertain systems. The uncertain parameters are assumed to be bounded by intervals. The computation of the controller is addressed by introducing the interval arithmetic. The controller synthesis is formulated as a set inversion problem that can be solved using the SIVIA algorithm. The proposed method is afterwards applied to design a robust controller for a piezoelectric microactuator. The experimental results show the efficiency of the proposed method. Finally, a fine stability analysis is performed to analytically prove the robustness of the designed controller. more...
Published: 2012
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23. Contractor programming

Author: Gilles Chabert, Luc Jaulin, Laboratoire d'Informatique de Nantes Atlantique (LINA), Centre National de la Recherche Scientifique (CNRS)-Mines Nantes (Mines Nantes)-Université de Nantes (UN), Développement des Technologies Nouvelles (DTN), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne) more...
Subjects: Constraint processing, 0209 industrial biotechnology, Linguistics and Language, Mathematical optimization, Set inversion, Formalism (philosophy), Intersection (set theory), Computer science, Solution set, 02 engineering and technology, Programming languages, Space (commercial competition), Solver, Deadlock, Solver design, Language and Linguistics, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Set (abstract data type), 020901 industrial engineering & automation, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, Interval methods, 020201 artificial intelligence & image processing
Abstract: WOS; International audience; This paper describes a solver programming method, called "contractor programming", that copes with two issues related to constraint processing over the reals. First, continuous constraints involve an inevitable step of solver design. Existing softwares provide an insufficient answer by restricting users to choose among a list of fixed strategies. Our first contribution is to give more freedom in solver design by introducing programming concepts where only configuration parameters were previously available. Programming consists in applying operators (intersection, composition, etc.) on algorithms called "contractors" that are somehow similar to propagators. Second, many problems with real variables cannot be cast as the search for vectors simultaneously satisfying the set of constraints, but a large variety of different outputs may be demanded from a set of constraints (e.g., a paving with boxes inside and outside of the solution set). These outputs can actually be viewed as the result of different "contractors" working concurrently on the same search space, with a bisection procedure intervening in case of deadlock. Such algorithms (which are not strictly speaking solvers) will be made easy to build thanks to a new branch & prune system, called "paver". Thus, this paper gives a way to deal harmoniously with a larger set of problems while giving a fine control on the solving mechanisms. The contractor formalism and the paver system are the two contributions. The approach is motivated and justified through different cases of study. An implementation of this framework named Quimper is also presented. more...
Published: 2009
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24. Optimal initial state for fast parameter estimation in nonlinear dynamical systems

Author: Qiaochu Li, Carine Jauberthie, Lilianne Denis-Vidal, Zohra Cherfi, Roberval ( LRURM ), Université de Technologie de Compiègne ( UTC ), Équipe DIagnostic, Supervision et COnduite ( LAAS-DISCO ), Laboratoire d'analyse et d'architecture des systèmes [Toulouse] ( LAAS ), Centre National de la Recherche Scientifique ( CNRS ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Institut National Polytechnique [Toulouse] ( INP ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Toulouse III - Paul Sabatier ( UPS ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Institut National Polytechnique [Toulouse] ( INP ), Laboratoire de Mathématiques Appliquées de Compiègne ( LMAC ), Roberval (Roberval), Université de Technologie de Compiègne (UTC), Équipe DIagnostic, Supervision et COnduite (LAAS-DISCO), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Laboratoire de Mathématiques Appliquées de Compiègne (LMAC), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées more...
Subjects: [ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC], 0209 industrial biotechnology, Mathematical optimization, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS], Initialization, Health Informatics, Context (language use), 02 engineering and technology, Interval (mathematics), [ SPI.SIGNAL ] Engineering Sciences [physics]/Signal and Image processing, Models, Biological, 030218 nuclear medicine & medical imaging, Interval arithmetic, 03 medical and health sciences, Glucose Oxidase, 020901 industrial engineering & automation, 0302 clinical medicine, Control theory, [ SPI.AUTO ] Engineering Sciences [physics]/Automatic, 0202 electrical engineering, electronic engineering, information engineering, Parameter estimation, Nonlinear systems, Interval analysis, Computer Simulation, Sensitivity (control systems), Contractor, Mathematics, Set inversion, Estimation theory, Sampling (statistics), [ SDV.SPEE ] Life Sciences [q-bio]/Santé publique et épidémiologie, [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], Optimal initial state, Computer Science Applications, Moment (mathematics), Bounded noise, Nonlinear system, Nonlinear Dynamics, Control and Systems Engineering, Bounded function, 020201 artificial intelligence & image processing, 030217 neurology & neurosurgery, Software, Algorithms
Abstract: International audience; Background and Objective: This paper deals with the improvement of parameter estimation in terms of precision and computational time for dynamical models in a bounded error context. Methods: To improve parameter estimation, an optimal initial state design is proposed combined with a contractor. This contractor is based on a volumetric criterion and an original condition initializing this contractor is given. Based on a sensitivity analysis, our optimal initial state design methodology consists in searching the minimum value of a proposed criterion for the interested parameters. In our framework, the uncertainty (on measurement noise and parameters) is supposed unknown but belongs to known bounded intervals. Thus guaranteed state and sensitivity estimation have been considered. An elementary effect analysis on the number of sampling times is also implemented to achieve the fast and guaranteed parameter estimation. Results: The whole procedure is applied to a pharmacokinetics model and simulation results are given. Conclusions: The good improvement of parameter estimation in terms of computational time and precision for the case study highlights the potential of the proposed methodology. more...
Published: 2015
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25. ROBUST NONLINEAR CONTINUOUS-TIME STATE ESTIMATION USING INTERVAL TAYLOR MODELS

Author: Yves Candau, Nacim Ramdani, Tarek Raïssi, Laboratoire d'Automatique, Productique et Signal (LAPS), Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-École Nationale d'Ingénieurs des Travaux Agricoles - Bordeaux (ENITAB)-Centre National de la Recherche Scientifique (CNRS), Artificial movement and gait restoration (DEMAR), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Interactive Digital Humans (IDH), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre d'Etudes et Recherches en Thermique, Environnement et Systèmes [Créteil] (CERTES EA 3481), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), Université Sciences et Technologies - Bordeaux 1 (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-École Nationale d'Ingénieurs des Travaux Agricoles - Bordeaux (ENITAB)-Centre National de la Recherche Scientifique (CNRS), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Inria Sophia Antipolis - Méditerranée (CRISAM), and Ramdani, Nacim more...
Subjects: 0209 industrial biotechnology, Set inversion, Estimator, Context (language use), 02 engineering and technology, General Medicine, Interval (mathematics), Interval arithmetic, Nonlinear system, 020901 industrial engineering & automation, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Ordinary differential equation, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, 020201 artificial intelligence & image processing, Robust control, [INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering, Mathematics
Abstract: International audience; In this paper, state estimation for non-linear continuous-time systems is considered in a bounded-error context. The studied systems are described by ordinary differential equations for which explicit solutions are not available. The state estimator built in this paper relies on a validated integration of the ordinary differential equations using Taylor models and on set inversion. This estimator generates the set of all state vectors that are consistent with the modelling hypotheses, the measured data and the noise prior bounds. This property makes the use of this estimator suitable in the field of robust control. To render this algorithm efficient when the initial state is approximately known, consistency techniques are used. An illustrative example is presented. more...
Published: 2006
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26. Quantified Set Inversion Algorithm with Applications to Control

Author: Luc Jaulin, Miguel A. Sainz, Josep Vehí, Pau Herrero, Ensta Bretagne, Stic Rems, Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne) more...
Subjects: 0209 industrial biotechnology, Mathematical optimization, Set inversion, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, Applied Mathematics, Linear system, Solution set, 02 engineering and technology, Constraint satisfaction, Interval arithmetic, Computational Mathematics, Range (mathematics), 020901 industrial engineering & automation, Modal, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Control (linguistics), [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Algorithm, ComputingMilieux_MISCELLANEOUS, Software, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing, Mathematics
Abstract: In this paper, a new algorithm based on Set Inversion techniques and Modal Interval Analysis is presented. This algorithm allows one to solve problems involving quantified constraints over the reals through the characterization of their solution sets. The presented methodology can be applied to a wide range of problems involving uncertain (non)linear systems. Finally, an advanced application is solved. more...
Published: 2005
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27. Set membership state and parameter estimation for systems described by nonlinear differential equations

Author: Yves Candau, Nacim Ramdani, and Tarek Raïssi
Subjects: Predictor–corrector method, 0209 industrial biotechnology, Mathematical optimization, Set inversion, Estimation theory, Differential equation, Ode, 02 engineering and technology, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Ordinary differential equation, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Initial value problem, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, Mathematics
Abstract: This paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous-time systems, in a bounded-error context. A state estimator based on a prediction-correction approach is given, where the prediction step consists in a validated integration of an initial value problem for an ordinary differential equation (IVP for ODE) using interval analysis and high-order Taylor models, while the correction step uses a set inversion technique. The state estimator is extended to solve the parameter estimation problem. An illustrative example is presented for each part. more...
Published: 2004
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28. Guaranteed robust nonlinear estimation with application to robot localization

Author: Luc Jaulin, E. Walter, Dominique Meizel, Michel Kieffer, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), and Gerard, Marie-Françoise more...
Subjects: 0209 industrial biotechnology, Mathematical optimization, [SPI] Engineering Sciences [physics], 02 engineering and technology, nonlinear estimation, Interval arithmetic, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, robot localization, Robustness (computer science), 0202 electrical engineering, electronic engineering, information engineering, bounded-error etsimation, Electrical and Electronic Engineering, Mathematics, Set inversion, set estimation, outliers, Estimator, robust estimation, set inversion, Computer Science Applications, Human-Computer Interaction, Data point, Control and Systems Engineering, Outlier, 020201 artificial intelligence & image processing, Set estimation, Robust control, interval analysis, Software, Information Systems
Abstract: International audience; when rliable prior bounds on the acceptable erors between the data and corresponding model outputs are availabl, bounded-error estimation techniques make it possible to characterize the set of all acceptable parameter vectors in a guaranteed way, ven when the model is nonlinear and the number of data points small. However, when the data may contain outliers, i.e., data points for which these bounds should be violated, this set may turn out to be empty, or a least unrealistically small. The outlier minimal number estimator (OMNE) has been designed to deal with such a situation, by minimizing the number of data points considered as outliers. OMNE has been shown in previous papers to be remarkbly robust, even to a majority of outliers. Up to now, it was implemented by random scanning, so its results could not be guaranteed. In this paper, a new algorithm based on set inversion via interval analysis provides a guaranteed OMNE, which is applied to the initial localization of an actual robot in a partially known 2D environment. The difficult problems of associating range data to landmarks of the environment and of detecting potential outliers are solved as by-products of the procedure. more...
Published: 2002
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29. Guaranteed estimation of electrochemical parameters by set inversion using interval analysis

Author: Michel Kieffer, Fabienne Berthier, Isabelle Braems, Luc Jaulin, E. Walter, Laboratoire d'étude des matériaux hors équilibre (LEMHE), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), and Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.) more...
Subjects: Electrochemical parameters, 0209 industrial biotechnology, Signal processing, Set inversion, Estimation theory, Chemistry, General Chemical Engineering, Initialization, Context (language use), 02 engineering and technology, 021001 nanoscience & nanotechnology, Analytical Chemistry, Interval arithmetic, Set (abstract data type), [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Electrochemistry, Interval analysis, Point estimation, 0210 nano-technology, Algorithm
Abstract: International audience; The bounded-error approach to parameter estimation, mainly developed in the context of control and signal processing, is applied in the electrochemistry field in order to obtain reliable estimates for kinetic parameters. The method is based on the assumption that an uncertainty bar is available for each measurement. A set guaranteed to contain all values of the parameter vector that lead to model outputs consistent with these error bars is then computed, based on interval analysis and set inversion. The resulting technique is applied on simulated and experimental data for several classical electrochemical models. Its merits are compared to those of a more traditional approach based on least square estimation by iterative local optimization. A first obvious difference is that the point estimate provided by the latter method may or may not belong to the set estimated by the former, because it does not take the bounds on the uncertainty into account. Moreover, as our approach is global, it escapes the difficult problem of initialization encountered with iterative optimization methods. Finally, the set obtained is a natural characterization of the uncertainty on the estimated parameters. more...
Published: 2000
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30. Set inversion for χ-algorithms, with application to guaranteed robot localization

Author: Luc Jaulin, Eric Walter, Dominique Meizel, O. Leveque, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Université d'Angers (UA), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA), and Gerard, Marie-Françoise more...
Subjects: 0209 industrial biotechnology, General Computer Science, [SPI] Engineering Sciences [physics], 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Theoretical Computer Science, Image (mathematics), Interval arithmetic, Set (abstract data type), [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, 0101 mathematics, Sequential algorithm, Mathematics, Numerical Analysis, Set inversion, Applied Mathematics, Robot localization, Function (mathematics), 16. Peace & justice, Nonlinear estimation, Range (mathematics), Modeling and Simulation, Robot, interval analysis, Algorithm, Bounded-error, Set-inversion
Abstract: International audience; Characterizing the set of all parameter vectors such that their image by a vector function belongs to a given set is a set-inversion problem. The algorithm SIVIA (Set Inversion Via Interval Analysis) makes it possible to perform this task in an approximate but guaranteed way. In the examples treated so far, the function to be inverted was given either explicitly or by a sequential algorithm. In this paper, this approach is extended to the case of branching algorithms involving if statements. As an illustration, the static localization of a robot from bounded-error range measurements is considered. The notion of remoteness, introduced for an archetypal but realistic sonar model, allows this problem to be cast into the set-inversion framework. more...
Published: 2000
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31. Guaranteed State and Parameter Estimation for Nonlinear Dynamical Aerospace Models

Author: Lilianne Denis-Vidal, Qiaochu Li, Zohra Cherfi, Carine Jauberthie, Roberval (Roberval), Université de Technologie de Compiègne (UTC), Équipe DIagnostic, Supervision et COnduite (LAAS-DISCO), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Laboratoire de Mathématiques Appliquées de Compiègne (LMAC), Équipe DIagnostic, Supervision et COnduite ( LAAS-DISCO ), Laboratoire d'analyse et d'architecture des systèmes [Toulouse] ( LAAS ), Centre National de la Recherche Scientifique ( CNRS ) -Université Toulouse III - Paul Sabatier ( UPS ), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Institut National Polytechnique [Toulouse] ( INP ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Toulouse III - Paul Sabatier ( UPS ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Institut National Polytechnique [Toulouse] ( INP ), Roberval, Université de Technologie de Compiègne ( UTC ), Laboratoire de Mathématiques Appliquées de Compiègne ( LMAC ), Laboratoire des Technologies Nouvelles ( INRETS/LTN ), Institut National de Recherche sur les Transports et leur Sécurité ( INRETS ), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées more...
Subjects: [ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC], 0209 industrial biotechnology, [ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS], Context (language use), [ SPI.SIGNAL ] Engineering Sciences [physics]/Signal and Image processing, 02 engineering and technology, 01 natural sciences, Interval arithmetic, 010104 statistics & probability, 020901 industrial engineering & automation, Control theory, [ SPI.AUTO ] Engineering Sciences [physics]/Automatic, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Parameter estimation, Nonlinear systems, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Interval analysis, 0101 mathematics, Aerospace models, Mathematics, Set inversion, Estimation theory, [ SDV.SPEE ] Life Sciences [q-bio]/Santé publique et épidémiologie, [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], Solver, 16. Peace & justice, Bounded noise, Continuous-time systems, Nonlinear system, Ordinary differential equation, Bounded function, State estimation
Abstract: International audience; This paper deals with parameter and state estimation in a bounded-error context for uncertain dynamical aerospace models when the input is considered optimized or not. In a bounded-error context, perturbations are assumed bounded but otherwise unknown. The parameters to be estimated are also considered bounded. The tools of the presented work are based on a guaranteed numerical set integration solver of ordinary differential equations combined with adapted set inversion computation. The main contribution of this work consists in developing procedures for parameter estimation whose performance is highly related with the input of system. In this paper, a comparison with a classical non-optimized input is proposed. more...
Published: 2014
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32. Fault detection using interval Kalman filtering enhanced by constraint propagation

Author: Louise Travé-Massuyès, Carine Jauberthie, Jun Xiong, Françoise Le Gall, Équipe DIagnostic, Supervision et COnduite (LAAS-DISCO), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT) more...
Subjects: 0209 industrial biotechnology, Set inversion, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Kalman filter, Invariant extended Kalman filter, Fault detection and isolation, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Extended Kalman filter, symbols.namesake, 020901 industrial engineering & automation, Control theory, Gaussian noise, 0202 electrical engineering, electronic engineering, information engineering, Local consistency, symbols, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, 020201 artificial intelligence & image processing, Fast Kalman filter, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; In this paper, we consider an extension of conventional Kalman filtering to discrete time linear models with bounded uncertainties on parameters and gaussian measurement noise. To solve the interval matrix inversion problem involved in the equations of the Kalman filter and the over-bounding problem due to interval calculus, we propose an original approach combining the set inversion algorithm SIVIA and constraint propagation. The improved interval Kalman filter is applied in a fault detection schema illustrated by a simple case study. more...
Published: 2013
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33. Improvements in computational aspects of Interval Kalman Filtering enhanced by constraint propagation

Author: Carine Jauberthie, Louise Travé-Massuyès, Jun Xiong, Équipe DIagnostic, Supervision et COnduite (LAAS-DISCO), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT) more...
Subjects: 0209 industrial biotechnology, Set inversion, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Kalman filter, Constraint satisfaction, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Extended Kalman filter, symbols.namesake, 020901 industrial engineering & automation, Control theory, Gaussian noise, 0202 electrical engineering, electronic engineering, information engineering, Local consistency, symbols, 020201 artificial intelligence & image processing, Fast Kalman filter, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Algorithm, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Constraint satisfaction problem, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; This paper deals with computational aspects of interval kalman filtering of discrete time linear models with bounded uncertainties on parameters and gaussian measurement noise. In this work, we consider an extension of conventional Kalman filtering to interval linear models [1]. As the expressions for deriving the Kalman filter involve matrix inversion which is known to be a difficult problem. One must hence find a way to implement or avoid this tricky algebraic operation within an interval framework. To solve the interval matrix inversion problem and other problems due to interval calculus, we propose an original approach combining the set inversion algorithm SIVIA and constraint satisfaction propagation. Several contractors are proposed to limit overestimation effects propagating within the interval Kalman filter recursive structure. Thus the description of our approach is followed by an application and we compare the proposed approach with interval kalman filtering developped in [1]. more...
Published: 2013

34. Design of Piezoelectric Actuators with Guaranteed Performances Using the Performances Inclusion Theorem

Author: Micky Rakotondrabe, Sofiane Khadraoui, Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174) (FEMTO-ST), Université de Technologie de Belfort-Montbeliard (UTBM)-Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Texas A&M University at Qatar, and Rakotondrabe Micky more...
Subjects: 0209 industrial biotechnology, Set inversion, Computer science, 02 engineering and technology, Interval (mathematics), 021001 nanoscience & nanotechnology, Transfer function, Piezoelectricity, Computer Science::Other, Interval arithmetic, 020901 industrial engineering & automation, Control theory, A priori and a posteriori, [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics, 0210 nano-technology, Actuator, Reference model
Abstract: International audience; This chapter presents the design of piezoelectric actuators by using the performances inclusion theorem (PIT). The main objective is to seek for the dimensions of a cantilevered actuator such that its performances will lie within some specifications imposed a priori. For that, these specifications are transcribed into an interval transfer function, called interval reference model, while an interval model of the actuator is also provided. Then, from the PIT, a problem of finding the dimensions is yielded such that this latter model is enclosed in the reference model. The problem is seen as a set-inversion problem that can be solved with interval tools such as the SIVIA (Set Inversion Via Interval Analysis) algorithms. The designed piezoelectric actuator is afterwards fabricated and characterized. The experimental characterizations demonstrate the efficiency of the proposed technique. more...
Published: 2013
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35. Reliable Positioning Domain Computation for Urban Navigation

Author: Vincent Drevelle, Philippe Bonnifait, Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), and ANR-10-EQPX-0044,ROBOTEX,Réseau national de plateformes robotiques d'excellence(2010) more...
Subjects: 050210 logistics & transportation, 0209 industrial biotechnology, Engineering, Set inversion, business.industry, Hybrid positioning system, Receiver autonomous integrity monitoring, Mechanical Engineering, 05 social sciences, Control engineering, 02 engineering and technology, Interval (mathematics), computer.software_genre, Precise Point Positioning, Computer Science Applications, Interval arithmetic, 020901 industrial engineering & automation, Assisted GPS, 0502 economics and business, Automotive Engineering, Global Positioning System, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Data mining, business, computer
Abstract: International audience; Reliable positioning is a key issue for intelligent vehicle navigation. Interval-based positioning methods have shown to be capable of computing relevant confidence domains used for integrity monitoring in environments which are challenging for Global Positioning System (GPS). The approach presented in this paper consists in tightly coupling a GPS receiver with a 3D-map of the drivable area. Interval analysis is employed to solve the constraint positioning problem using contractions and bisections. Integrity is provided through the use of a robust set inversion scheme applied to a redundant measurement set. If the prior distribution of the measurement noise is known, it is possible to compute confidence domains that correspond to a given integrity risk, which is often set very low out of safety considerations. In this paper we examine a way of validating the proposed approach, using a real experimental dataset and a ground truth equipment. Different tunings of the method, corresponding to different risks, are assessed in terms of availability and integrity in order to compute statistical metrics. Results indicate that this methodology is relevant since the specified risk corresponds to experimental observations. more...
Published: 2013
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36. A new interval-based method to characterize estimability

Author: Luc Jaulin, Olivier Reynet, Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), and École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)
Subjects: 0209 industrial biotechnology, experimental design, Computer science, estimability, 02 engineering and technology, Interval (mathematics), Interval arithmetic, 020901 industrial engineering & automation, 0203 mechanical engineering, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Statistics, Applied mathematics, Electrical and Electronic Engineering, bounded-error estimation, 020301 aerospace & aeronautics, Set inversion, Estimation theory, 16. Peace & justice, Multilateration, identifiability, worst-case design, Nonlinear system, Control and Systems Engineering, Bounded function, Signal Processing, Identifiability, interval analysis, nonlinear models, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract: SUMMARYEstimability is a property which states on the accuracy of the parameter estimation in the case ofexperimental data. This paper de nes a new method based on interval analysis and set inversion tocharacterize estimability in the case of a bounded additive noise. To illustrate this new method, theTime Di erence of Arrival (TDOA) passive location estimability is evaluated: to our knowledge, it isthe rst time that the parameter estimation error of these nonlinear equations is given. Copyright c2010 John Wiley & Sons, Ltd.key words: Estimability, Identi ability, Interval Analysis, nonlinear Models, Experimental Design. 1. IntroductionEstimability is a property which states on the accuracy of the parameter estimation in the caseof experimental data [1, 2]. Indeed, a parameter can be identi able [3, 4] but poorly estimable Correspondence to: Olivier Reynet (olivier.reynet@ensieta.fr) at E 3 I 2 laboratory - ENSIETA - 2, rue F. Verny- 29806 Brest Cedex 9 - www.ensieta.fr Copyright c 2010 John Wiley & Sons, Ltd. more...
Published: 2011
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37. Guaranteed set-point computation with application to the control of a sailboat

Author: Pau Herrero, Luc Jaulin, Josep Vehí, Miguel A. Sainz, Extraction et Exploitation de l'Information en Environnements Incertains (E3I2), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Universitat de Girona, and Universitat de Girona (UdG) more...
Subjects: 0209 industrial biotechnology, Mathematical optimization, Class (set theory), feedback linearization, Set inversion, 02 engineering and technology, Solver, Nonlinear control, 16. Peace & justice, Computer Science Applications, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), 020901 industrial engineering & automation, non-linear control, Control and Systems Engineering, Quantifier elimination, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Feedback linearization, interval analysis, Algorithm, set computation, Mathematics
Abstract: WOS; International audience; The problem of characterizing in a guaranteed way the set of all feasible set-points of a control problem is known to be difficult. In the present work, the problem to be solved involves non-linear equality constraints with variables affected by logical quantifiers. This problem is not solvable by current symbolic methods like quantifier elimination, which is commonly used for solving this class of problems. We propose the utilization of guaranteed set-computation techniques based on interval analysis, in particular a solver referred to as Quantified Set Inversion (QSI). As an application example, the problem of simultaneously controlling the speed and the orientation of a sailboat is presented. For this purpose, the combination of QSI solver and feedback linearization techniques is employed. more...
Published: 2010
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38. State estimation by interval analysis for a nonlinear differential aerospace model

Author: Louise Travé-Massuyès, Pauline Ribot, Carine Jauberthie, Équipe DIagnostic, Supervision et COnduite (LAAS-DISCO), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées more...
Subjects: 0209 industrial biotechnology, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Context (language use), 02 engineering and technology, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Nonlinear systems, Interval analysis, Differential (infinitesimal), Aerospace, Mathematics, Set inversion, business.industry, 020208 electrical & electronic engineering, 16. Peace & justice, Nonlinear system, Continuous-time systems, Bounded noise, Ordinary differential equation, Bounded function, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], business, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, State estimation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; This paper deals with guaranteed state estimation in a bounded-error context for an aerospace model. Perturbations are assumed bounded but otherwise unknown. The main tools to solve this problem are the guaranteed techniques for ordinary differential equation integration and set inversion. The obtained results show the efficiency of the method. more...
Published: 2007

39. Initial localization by set inversion

Author: Luc Jaulin, O. Leveque, Dominique Meizel, E. Walter, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), and Gerard, Marie-Françoise more...
Subjects: 0209 industrial biotechnology, Set inversion, Matching (graph theory), Mobile robot, 02 engineering and technology, Nonlinear system, Range (mathematics), 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Salient, Outlier, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Set theory, Electrical and Electronic Engineering, Algorithm, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: In this paper, initial localization problems are solved by using set-membership estimation. The method can be used with any robot and any kind of sensor(s), provided that a computable model of the environment/sensor interaction is available. With a pedagogical aim in mind, it is detailed in the case of the localization of a vehicle from range measurements in a polygonal environment. Salient properties of the method are as follows. First, it does not need any explicit management of matching hypotheses. Second, it is able to deal with ambiguous situations where several radically different vehicle configurations are consistent with the measurements. Third, it can be made robust to outliers. Fourth, it can deal with nonlinear observation models without any approximation. Fifth, the result is guaranteed in the sense that no configuration consistent with the data and the hypotheses can be missed. more...
Published: 2002

40. Guaranteed Set Computation with Subpavings

Author: Michel Kieffer, Eric Walter, Luc Jaulin, Isabelle Braems, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA), Laboratoire d'étude des matériaux hors équilibre (LEMHE), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), W. KRAEMER and J.W. GUDENBERG, Kluwer Academic Publishers, and Boston/Dordrecht/London more...
Subjects: 0209 industrial biotechnology, Theoretical computer science, Binary tree, Set inversion, Intersection (set theory), Computation, 020208 electrical & electronic engineering, trees, 02 engineering and technology, Binary trees, set inversion, 16. Peace & justice, Image (mathematics), Set (abstract data type), [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Simple (abstract algebra), bounded errors, 0202 electrical engineering, electronic engineering, information engineering, image evaluation, recursive algorithms, subpavings, Representation (mathematics), Mathematics
Abstract: International audience; This paper is about the approximate representation of compact sets using subpavings, i.e., unions of non-overlapping boxes, and about computation on these sets, with particular attention to implementation issues. Some basic operations such as evaluating the intersection or union of two subpavings, or testing whether a box belongs to a subpaving are first presented. The binary tree structure used to describe subpavings then allows a simple implementation of these tasks by recursive algorithms. Algorithms are presented to evaluate the inverse and direct images of a set described by a subpaving. In both cases, a subpaving is obtained that is guaranteed to contain the actual inverse or direct image of the initial subpaving. The effectiveness of these algorithms in characterizing possibly nonconvex on even nonconnected stes is finally illustrated by simple examples. more...
Published: 2001
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41. Interval constraint propagation with application to bounded-error estimation

Author: Luc Jaulin, Gerard, Marie-Françoise, Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), and Université d'Angers (UA) more...
Subjects: 0209 industrial biotechnology, Mathematical optimization, Set inversion, Estimation theory, [SPI] Engineering Sciences [physics], Feasible region, 02 engineering and technology, Interval (mathematics), Parameter space, Constraint propagation, Interval arithmetic, Nonlinear programming, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Bounded-error estimation, Control and Systems Engineering, 0202 electrical engineering, electronic engineering, information engineering, Local consistency, Interval analysis, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, Nonlinear constraint solving, Mathematics
Abstract: International audience; For a large class of bounded-error estimation problems, the posterior feasible set S for the parameters can be defined by nonlinear inequalities. The set-inversion approach combines classical interval analysis with branch-and-bound algorithms to characterize S. Unfortunately, as bisections have to be done in all directions of the parameter space, this approach is limited to problems involving a small number of parameters. Techniques based on interval constraint propagation make it possible to drastically reduce the number of bisections. In this paper, these techniques are combined with set inversion to bracket S between inner and outer subpavings (union of nonoverlapping boxes). When only interested ine the feasible intervals for the parameters, the set inversion approach becomes inefficient, and a new algorithm able to compute these intervals is given. This algorithm uses a new interval-based local research to compute the smallest box that contains S. It is then compared with existing methods on an example taken from the literature. more...
Published: 2000

42. Comparison of two calculation methods of the optimal switching instants of a hybrid dynamic system

Author: Manuela Sechilariu, Benoit Cebron, Jacques Burger, Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Université d'Angers (UA), AVENUES (AVENUES), Université de Technologie de Compiègne (UTC), and Sechilariu, Manuela more...
Subjects: 0209 industrial biotechnology, Automatic control, Set inversion, [SPI] Engineering Sciences [physics], 020208 electrical & electronic engineering, Minimization problem, 02 engineering and technology, Optimal control, Calculation methods, Interval arithmetic, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Control theory, Control system, 0202 electrical engineering, electronic engineering, information engineering, symbols, Lagrangian, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: Two calculation methods of the optimal switching instants of a hybrid dynamic system are presented. The control problem is set as a minimization problem of the deviation between the state and a desired state, at the final instant. The first method uses the Lagrangian technique to calculate the gradient of a cost function and implements the Fletcher-Reeves descent method (Minoux, 1983). The second method is based on interval analysis. The set inversion algorithm SIVIA (Jaulin and Burger, 1999) which is presented and implemented, ensures guaranteed results. Both methods are applied to an example then compared. more...
Published: 1999

43. Guaranteed recursive nonlinear state estimation using interval analysis

Author: Michel Kieffer, Luc Jaulin, E. Walter, Laboratoire d'Ingéniérie des Systèmes Automatisés (LISA), Centre National de la Recherche Scientifique (CNRS)-Université d'Angers (UA), Département STIC [Brest] (STIC), École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), and Gerard, Marie-Françoise more...
Subjects: 0209 industrial biotechnology, Mathematical optimization, Noise measurement, Set inversion, [SPI] Engineering Sciences [physics], Linear model, Estimator, 02 engineering and technology, Interval (mathematics), Interval arithmetic, Set (abstract data type), Noise, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, 020201 artificial intelligence & image processing, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: International audience; The problem considered is state estimation in the presence of unknow state and measurement noise, each noise component being assumed to belong to some known interval. In such a bounded-error context, most available results are for linear models, and the purpose of the present paper is to deal with the nonlinear case. Based on interval analysis and the notion of set inversion, a new state estimator is presented, which evaluates a set estimate guaranteed to contain all values of the states that are consistent with the available observations, given the noise bounds and a set containing the initial value of the state. To the best of our knowledge, it is the first time that such a guaranteed estimator is made available. The precision of the set estimate can be improved, at the cost of more computation. The theorical properties of the estimator are studied, and computer implementation has received special attention. A simple illustrative example is treated. more...
Published: 1998

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