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1. An adaptive observer for sensor fault estimation in a class of uniformly observable nonlinear systems

Author

Qinghua Zhang, Gildas Besancon, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Grenoble Images Parole Signal Automatique (GIPSA-lab), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Observer (quantum physics), Applied Mathematics, 020208 electrical & electronic engineering, FDI, non-linear system, 02 engineering and technology, Fault (power engineering), high gain observer, Fault detection and isolation, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, adaptive observer, Nonlinear system, 020901 industrial engineering & automation, Control theory, Modeling and Simulation, Convergence (routing), Parametric model, 0202 electrical engineering, electronic engineering, information engineering, State observer, Fault Detection and Isolation, Alpha beta filter, Mathematics
Abstract

International audience; Based on the techniques of high gain observer and adaptive estimation, an adaptive observer is proposed in this paper for sensor fault estimation in a class of uniformly observable non-linear systems. It is first assumed that a high gain observer exists for the fault-free system. With a parametric model of sensor fault, a high gain adaptive observer is then designed for sensor fault estimation. In order to establish the global convergence of the adaptive observer, in addition to the usual conditions for high gain observer convergence, a persistent excitation condition is also required, like in most recursive parameter estimation problems.

Published
2008

2. Extremum seeking via continuation techniques for optimizing biogas production in the chemostat

Author

Jan Sieber, Serafim Rodrigues, Mathieu Desroches, Alain Rapaport, Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), 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)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), College of Engineering, Mathematics and Physical Sciences [Exeter] (EMPS), University of Exeter, Centre for Robotics and Neural Systems (CRNS), Plymouth University, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)

Subjects
adaptive control, self-optimizing control, parameter optimization, biotechnology, 0209 industrial biotechnology, Mathematical optimization, Adaptive control, Steady state (electronics), optimisation, Automatic, 02 engineering and technology, Chemostat, 7. Clean energy, symbols.namesake, Continuation, 020901 industrial engineering & automation, 020401 chemical engineering, Control theory, FOS: Mathematics, Production (economics), 0204 chemical engineering, Mathematics - Optimization and Control, Automatique / Robotique, Newton's method, SIMPLE algorithm, Mathematics, chemostat, calcul automatique, General Medicine, biogaz, mathématiques appliquées, Numerical continuation, Optimization and Control (math.OC), Autre (Sciences de l'ingénieur), symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], algorithme
Abstract

International audience; We consider the chemostat model with the substrate concentration as the single measurement. We propose a control strategy that drives the system at a steady state maximizing the gas production without the knowledge of the specific growth rate. Our approach separates the extremum seeking problem from the feedback control problem such that each of the two subproblems can be solved with relatively simple algorithms. We are then free to choose any numerical optimization algorithm. We give a demonstration for two choices: one is based on slow-fast dynamics and numerical continuation, the other is a combination of golden-section and Newton iteration. The method copes with non-monotonic growth functions.

Published
2013

3. Fault diagnosis for linear time-varying descriptor systems

Author

Abdouramane Moussa Ali, Qinghua Zhang, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Statistical Inference for Structural Health Monitoring (I4S), Département Composants et Systèmes (IFSTTAR/COSYS), PRES Université Lille Nord de France-PRES Université Nantes Angers Le Mans (UNAM)-Université de Lyon-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-PRES Université Lille Nord de France-PRES Université Nantes Angers Le Mans (UNAM)-Université de Lyon-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Inria Rennes – Bretagne Atlantique, Giri, Fouad and Van Assche, Vincent, Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Département Composants et Systèmes (IFSTTAR/COSYS), PRES Université Lille Nord de France-PRES Université Nantes Angers Le Mans (UNAM)-Université de Lyon-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-PRES Université Lille Nord de France-PRES Université Nantes Angers Le Mans (UNAM)-Université de Lyon-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR), and Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université de Lyon-PRES Université Nantes Angers Le Mans (UNAM)-PRES Université Lille Nord de France-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université de Lyon-PRES Université Nantes Angers Le Mans (UNAM)-PRES Université Lille Nord de France-Inria Rennes – Bretagne Atlantique

Subjects
0209 industrial biotechnology, Descriptor systems, 02 engineering and technology, fault diagnosis, Fault (power engineering), [SPI.AUTO]Engineering Sciences [physics]/Automatic, adaptive observer, discrete-time descriptor dynamics, time-varying models, 020901 industrial engineering & automation, Discrete time and continuous time, Control theory, 0202 electrical engineering, electronic engineering, information engineering, State space, 020201 artificial intelligence & image processing, Gravitational singularity, Actuator, Time complexity, Mathematics, Parametric statistics
Abstract

International audience; In this paper fault diagnosis is studied for linear time varying descriptor systems, which are the discrete time counterpart of the continuous time dynamic systems described by differential-algebraic equations. This class of systems includes and is broader than the well-known state space systems. The framework of descriptor systems is particularly useful for studying dynamic systems exhibiting time varying singularities. Actuator faults and sensor faults are respectively modeled as parametric changes in the state equation and in the output equation. The main result of this paper consists in extending an adaptive observer, initially designed for state space systems, to descriptor systems. Based on this result, fault diagnosis is performed by estimating the parameters characterizing actuator and sensor faults.

Published
2013

4. Identification of an extended Hammerstein system with input hysteresis nonlinearity for control valve stiction characterization

Author

Jiandong Wang, Qinghua Zhang, College of Engineering [Beijing], Peking University [Beijing], SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Kinnaert, Michel, and ANR-10-INTB-0201,EBONSI,Identification de systèmes non linéaires par modules inter-connectés étendus(2010)

Subjects
Control valves, 0209 industrial biotechnology, Engineering, Nonlinear system identification, Control valve stiction, business.industry, Iterative method, Hysteresis model, System identification, Nonlinear System Identification, Closed Loop Identification, 020206 networking & telecommunications, 02 engineering and technology, General Medicine, Parameter identification problem, Nonlinear system, Hysteresis, 020901 industrial engineering & automation, Closed-loop oscillation, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Stiction, 0202 electrical engineering, electronic engineering, information engineering, business
Abstract

International audience; The study in this paper is motivated by the modeling of control valves with significant stiction. By assuming linear dynamics of the controlled process, the joint characterization of the control valve and of the controlled process is formulated as the identification of an extended Hammerstein system. A point-slope-based hysteresis model is used to describe the input hysteresis nonlinearity of the control valve. An iterative algorithm is proposed to solve the identification problem. The basic idea is to separate the ascent and descent paths of the input hysteresis nonlinearity subject to oscillatory excitations. Some identifiability analysis is performed: the proposed extended Hammerstein model structure is identifiable, and given the true input nonlinearity, the oscillatory signals in feedback control loops are shown to be informative by exploiting the cyclo-stationarity of these oscillatory signals. Industrial examples are provided to verify the effectiveness of the proposed identification algorithm in characterizing complicated characteristics of control valve stiction in practice.

Published
2012

5. Statistical fault detection and isolation for linear time-varying systems

Author

Qinghua Zhang, Michèle Basseville, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-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 (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and 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)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Engineering, business.industry, 020208 electrical & electronic engineering, 02 engineering and technology, General Medicine, Fault (power engineering), Stability (probability), Fault detection and isolation, Computer Science::Hardware Architecture, 020901 industrial engineering & automation, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Recursive filter, business, Computer Science::Operating Systems, Time complexity, Computer Science::Distributed, Parallel, and Cluster Computing, Parametric statistics
Abstract

International audience; This paper describes a statistical approach to fault detection and isolation for linear time-varying (LTV) systems subject to parametric additive faults. The proposed approach combines a GLR test with a recursive filter that cancels out the dynamics of the monitored faults effects. To our knowledge, the proposed recursive filter is new for the considered faults with time-varying profiles. The resulting algorithm handles fault diagnosis with weaker assumptions than usual, in particular on the number of sensors and on the stability of the monitored system.

Published
2012

6. Revisiting Hammerstein system identification through the Two-Stage Algorithm for bilinear parameter estimation

Author

Qinghua Zhang, Jiandong Wang, Lennart Ljung, Peking University [Beijing], SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Linköping University (LIU)

Subjects
0209 industrial biotechnology, Nonlinear system identification, Estimation theory, Generalization, 020208 electrical & electronic engineering, System identification, 02 engineering and technology, 16. Peace & justice, Weighting, Noise, 020901 industrial engineering & automation, Control and Systems Engineering, Colors of noise, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Non-linear least squares, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Electrical and Electronic Engineering, Mathematics
Abstract

International audience; The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the case of some special weighting matrices, the unweighted TSA is usually used in practice. It is shown in this paper that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least squares problem formulated with a particular weighting matrix. This provides a theoretical justification of the unweighted TSA, and also leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identification of Hammerstein systems are presented to validate the theoretical analysis.

Published
2009

7. Fuzzy model validation using the local statistical approach

Author

Qinghua Zhang, Gerasimos Rigatos, Industrial Systems Institute [Patras] (ISI), University of Patras [Greece], SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and University of Patras

Subjects
0209 industrial biotechnology, Mathematics::General Mathematics, Logic, Fuzzy set, 02 engineering and technology, computer.software_genre, Machine learning, Fuzzy logic, Fault detection and isolation, symbols.namesake, 020901 industrial engineering & automation, Artificial Intelligence, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Fisher information, Mathematics, Adaptive neuro fuzzy inference system, Fuzzy rule, business.industry, 020208 electrical & electronic engineering, Information processing, Fuzzy control system, ComputingMethodologies_PATTERNRECOGNITION, symbols, Artificial intelligence, Data mining, business, computer
Abstract

International audience; The local statistical approach for fault detection and isolation is applied to fuzzy models validation. The method detects the inconsistencies between a fuzzy rule base and the modelled system. It can also identify which are the faulty parameters of the fuzzy model. The Fisher information matrix explains the detectability of changes in the parameters of the fuzzy model. Simulation tests illustrate the method's credibility.

Published
2009

8. Optimality analysis of the Two-Stage Algorithm for Hammerstein system identification

Author

Qinghua Zhang, Jiandong Wang, Lennart Ljung, Peking University [Beijing], SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Linköping University (LIU)

Subjects
0209 industrial biotechnology, Mathematical optimization, Generalization, System identification, Parameterized complexity, TEKNIKVETENSKAP, 020206 networking & telecommunications, 02 engineering and technology, General Medicine, Weighting, Nonlinear system identification, Nonlinear system, Matrix (mathematics), Noise, 020901 industrial engineering & automation, Colors of noise, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, TECHNOLOGY, Mathematics
Abstract

International audience; The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the case of some special weighting matrices, the unweighted TSA is usually used in practice. It is shown in this paper that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least-squares problem formulated with a particular weighting matrix. This provides a theoretical justification of the unweighted TSA, and leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identification of Hammerstein systems are presented to validate the theoretical analysis.

Published
2009

9. Parsimonious Representation of Signals Based on Scattering Transform

Author

Qinghua Zhang, Taous-Meriem Laleg, Emmanuelle Crépeau, Michel Sorine, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques de Versailles (LMV), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Mathematical optimization, Signal processing, Inverse scattering transform, 010102 general mathematics, Feature extraction, 02 engineering and technology, General Medicine, Eigenfunction, 01 natural sciences, 020901 industrial engineering & automation, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0101 mathematics, Representation (mathematics), Algorithm, Eigenvalues and eigenvectors, Data compression, Mathematics, Interpolation
Abstract

International audience; A parsimonious representation of signals is a mathematic model parametrized with a small number of parameters. Such models are useful for analysis, interpolation, filtering, feature extraction, and data compression. A new parsimonious model is presented in this paper based on scattering transforms. It is closely related to the eigenvalues and eigenfunctions of the linear Schrödinger equation. The efficiency of this method is illustrated in this paper with examples of both synthetic and real signals.

Published
2008

10. A METHOD FOR ACTUATOR FAULT DIAGNOSIS WITH ROBUSTNESS TO SENSOR DISTORTION

Author

Qinghua Zhang, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Zhang Zhang

Subjects
0209 industrial biotechnology, Engineering, sensor distortion, Computer science, robustness, 02 engineering and technology, 01 natural sciences, 010104 statistics & probability, 020901 industrial engineering & automation, Control theory, Robustness (computer science), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Computer Science::Networking and Internet Architecture, Electronic engineering, Redundancy (engineering), ComputerSystemsOrganization_SPECIAL-PURPOSEANDAPPLICATION-BASEDSYSTEMS, 0101 mathematics, business.industry, General Medicine, fault diagnosis, Soft sensor, Actuator fault, Stuck-at fault, Nonlinear system, actuator fault, business
Abstract

Actuator fault diagnosis is often studied under strong assumptions on available sensors: typically it is assumed that either the sensors are fault-free or there is a sufficient redundancy among the sensors. The purpose of this paper is to propose a new method for actuator fault diagnosis which is robust to sensor distortion. It does not require sensor redundancy to compensate sensor distortion. The essential assumption is that sensor distortions are strictly monotonous. Despite the nonlinear and unknown nature of distortions, such sensors still provide useful information for fault diagnosis. A numerical example is provided to illustrate the efficiency of the proposed method. Copyright © 2006 IFAC

Published
2006

11. IDENTIFICATION OF WIENER SYSTEM WITH MONOTONOUS NONLINEARITY

Author

Anatoli Iouditski, Qinghua Zhang, Lennart Ljung, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Information Coding - Department of Electrical Engineering [Linköping] (ISY/ICG), Linköping University (LIU), and Brett Ninness and Håkan Hjalmarsson

Subjects
0209 industrial biotechnology, Nonlinear system identification, Gaussian, 020208 electrical & electronic engineering, Order (ring theory), quadratic programming, 02 engineering and technology, General Medicine, Wiener system, Signal, Nonlinear system, Identification (information), symbols.namesake, 020901 industrial engineering & automation, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, symbols, nonlinear system identification, Quadratic programming, Parametrization, Mathematics
Abstract

International audience; A Wiener system is composed of a linear dynamic subsystem followed by a static nonlinearity. It is well known in the literature that the identification of the linear subsystem of a Wiener system can be separated from that of the output nonlinearity, if the input signal is a Gaussian noise. In order to deal with the non Gaussian input case, two new algorithms are proposed in this paper for direct identification of the linear subsystem, regardless of any parametrization of the output nonlinearity. The essential assumption required in this paper is the strict monotonousness of the output nonlinearity.

Published
2006

12. Kalman Filter for Process Noise Free Systems

Author

Qinghua Zhang, Boyi Ni, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Giri, Fouad and Van Assche, and Vincent

Subjects
0209 industrial biotechnology, 020208 electrical & electronic engineering, 02 engineering and technology, General Medicine, Kalman filter, Adaptive filtering, Linear-quadratic-Gaussian control, Invariant extended Kalman filter, Fast algorithms, Extended Kalman filter, 020901 industrial engineering & automation, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Fast Kalman filter, Ensemble Kalman filter, Observability, Alpha beta filter, Mathematics
Abstract

International audience; The purpose of this paper is to study the stability properties of the Kalman filter applied to process noise free systems. Due to the absence of the process noise (also known as state noise), such a system cannot be controllable regarding the process noise. The stability of the Kalman filter is typically based on the boundedness of the error covariance matrix governed by a dynamic Riccati equation (DRE), which is usually ensured by the controllability regarding the process noise and by the observability. This classical result cannot be applied to the considered case because of the lack of controllability. It is shown in this paper that, under the observability condition, the solution of the DRE is bounded and converges to a solution of the algebraic Riccati equation (ARE), regardless of the stability of the considered system. In the case of asymptotically unstable systems, the solution of the ARE is not unique. In this case the relationship between the DRE and the ARE is clarified. It is also shown that the DRE based Kalman filter is always valid, whereas the ARE based Kalman filter cannot be applied when the process noise free system has marginally stable modes. A numerical example is presented to verify the correctness of the theoretical analysis.

Published
2013

13. Single minimum nonlinearity Wiener system identification by weighted principal component analysis

Author

Vincent Laurain, Qinghua Zhang, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Giri, Fouad and Van Assche, and Vincent

Subjects
0209 industrial biotechnology, Nonlinear system identification, Finite impulse response, Wiener filter, System identification, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Wiener deconvolution, 020206 networking & telecommunications, 02 engineering and technology, General Medicine, symbols.namesake, Nonlinear system, 020901 industrial engineering & automation, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, symbols, Classical Wiener space, Applied mathematics, Infinite impulse response, Mathematics
Abstract

International audience; Wiener system identification with a finite impulse response (FIR) model is investigated in this paper, focusing on the challenging case of non Gaussian input distribution and non monotonic nonlinearity. The proposed method assumes that the static nonlinear function of the Wiener system has a single minimum (or maximum), but does not assume any parametrization of the nonlinear function. Based on a modified principal component analysis (PCA), referred to as weighted PCA, the FIR coefficients of the Wiener system are estimated without estimating the nonlinear function of the Wiener system. The numerical computation cost is essentially equivalent to those of two standard PCA. Numerical examples in harsh practical conditions, with data generated by Wiener systems involving a discontinuous nonlinear function or an infinite impulse response, are presented to illustrate the robustness and effectiveness of the proposed method.

Published
2013

14. Feedback stabilization of discrete-time quantum systems subject to non-demolition measurements with imperfections and delays

Author

Hadis Amini, Igor Dotsenko, C. Sayrin, Ram Somaraju, Pierre Rouchon, Mazyar Mirrahimi, Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Applied Physics and Photonics [Brussels] (TONA), Vrije Universiteit Brussel (VUB), Laboratoire Kastler Brossel (LKB (Lhomond)), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Kastler Brossel (LKB [Collège de France]), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Collège de France (CdF (institution)), Mines Paris - PSL (École nationale supérieure des mines de Paris), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Collège de France (CdF (institution))-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Collège de France (CdF (institution))

Subjects
0209 industrial biotechnology, Markov process, 02 engineering and technology, 01 natural sciences, symbols.namesake, 020901 industrial engineering & automation, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Control theory, 0103 physical sciences, Quantum system, FOS: Mathematics, Statistical physics, Electrical and Electronic Engineering, 010306 general physics, Mathematics - Optimization and Control, Mathematics, Markov chain, Stochastic matrix, Cavity quantum electrodynamics, Observable, Metzler matrix, Control and Systems Engineering, Optimization and Control (math.OC), symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Stationary state
Abstract

We consider a controlled quantum system whose finite dimensional state is governed by a discrete-time nonlinear Markov process. In open-loop, the measurements are assumed to be quantum non-demolition (QND). The eigenstates of the measured observable are thus the open-loop stationary states: they are used to construct a closed-loop supermartingale playing the role of a strict control Lyapunov function. The parameters of this supermartingale are calculated by inverting a Metzler matrix that characterizes the impact of the control input on the Kraus operators defining the Markov process. The resulting state feedback scheme, taking into account a known constant delay, provides the almost sure convergence of the controlled system to the target state. This convergence is ensured even in the case where the filter equation results from imperfect measurements corrupted by random errors with conditional probabilities given as a left stochastic matrix. Closed-loop simulations corroborated by experimental data illustrate the interest of such nonlinear feedback scheme for the photon box, a cavity quantum electrodynamics system., Comment: submitted (16 pages, 4 figures)

Published
2013

15. Hamiltonian identification through enhanced observability utilizing quantum control

Author

Herschel Rabitz, Zaki Leghtas, Pierre Rouchon, Gabriel Turinici, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Department of Chemistry, Princeton University, Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), and Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
0209 industrial biotechnology, Hamiltonian identification, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], FOS: Physical sciences, 02 engineering and technology, 01 natural sciences, symbols.namesake, 020901 industrial engineering & automation, Ramsey interferometry, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], 0103 physical sciences, Quantum system, Observability, Statistical physics, Electrical and Electronic Engineering, 010306 general physics, Quantum, Physics, Quantum Physics, Observable, Quantum control, Computer Science Applications, Arbitrarily large, Dipole, Control and Systems Engineering, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Quantum Physics (quant-ph), Hamiltonian (quantum mechanics)
Abstract

This paper considers Hamiltonian identification for a controllable quantum system with non-degenerate transitions and a known initial state. We assume to have at our disposal a single scalar control input and the population measure of only one state at an (arbitrarily large) final time T. We prove that the quantum dipole moment matrix is locally observable in the following sense: for any two close but distinct dipole moment matrices, we construct discriminating controls giving two different measurements. Such discriminating controls are constructed to have three well defined temporal components, as inspired by Ramsey interferometry. This result suggests that what may appear at first to be very restrictive measurements are actually rich for identification, when combined with well designed discriminating controls, to uniquely identify the complete dipole moment of such systems. The assessment supports the employment of quantum control as a promising means to achieve high quality identification of a Hamiltonian., Submitted to IEEE TAC special issue on quantum control

Published
2012

16. Diagnosis of Inhomogeneous Insulation Degradation in Electric Cables by Distributed Shunt Conductance Estimation

Author

Qinghua Zhang, Huaibin Tang, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Shandong University, and ANR-08-SEGI-0009,INSCAN,Diagnostic de câbles électriques sécuritaires pour grandes infrastructures(2008)

Subjects
0209 industrial biotechnology, Engineering, 020209 energy, Insulator (electricity), 02 engineering and technology, Telegrapher's equations, Dielectric, 020901 industrial engineering & automation, Linearization, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Fault diagnosis, business.industry, Applied Mathematics, Conductance, Kalman filter, Distributed parameter estimation, 021001 nanoscience & nanotechnology, Computer Science Applications, Electric cables, Control and Systems Engineering, 0210 nano-technology, business, Shunt (electrical), Voltage
Abstract

International audience; For the diagnosis of inhomogeneous insulation degradation in electrical cables, the estimation of the distributed shunt conductance is studied in this paper. Gradual growth of the shunt conductance is a consequence of degradation of the dielectric properties of the insulator. The proposed estimation method is based on voltage and current measurements at a single end of the cable. After the linearization of the bilinear term of the telegrapher's equations through a perturbation approach, the Kalman filter is applied to transform the problem of dynamic system parameter estimation to a simple linear regression problem. Results of numerical simulations are presented to demonstrate the feasibility of the proposed method. In particular, it is shown that the weak sensitivity of the available measurements to the shunt conductance can be compensated by long time data samples.

Published
2012

17. A Kalman pre-filtered IV-based approach to continuous-time Hammerstein-Wiener system identification

Author

Hugues Garnier, Qinghua Zhang, Boyi Ni, Marion Gilson, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Michel Kinnaert

Subjects
Recursive estimation, 0209 industrial biotechnology, Hammerstein-Wiener models, Instrumental variable, Monte Carlo method, System identification, Monotonic function, 02 engineering and technology, General Medicine, Filter (signal processing), Kalman filter, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Parameter identification problem, Nonlinear system, Continuous-time systems, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Nonlinear systems, Iterative estimation, 020201 artificial intelligence & image processing, Mathematics
Abstract

International audience; This paper studies the identification problem for a class of Hammerstein-Wiener continuous- time systems, with a monotonic nonlinear function for the Wiener part. Based on the previously developed simplified refined instrumental variable method, and by making use of an adaptive observer for data filtering, a combined approach, referred to as the Kalman pre-filtered instrumental variable based method, is proposed. By taking the advantages of the two aforementioned methods, the new method is faster and has a naturally stabilized filter, as well as keeps a high estimation accuracy in most cases. Monte Carlo simulation analysis is used to illustrate the performances of the proposed methods.

Published
2012

18. A new method for the reconstruction of unknown non-monotonic growth functions in the chemostat

Author

Mathieu Desroches, Jan Sieber, Serafim Rodrigues, Alain Rapaport, College of Engineering, Mathematics and Physical Sciences [Exeter] (EMPS), University of Exeter, Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), 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)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre for Robotics and Neural Systems (CRNS), Plymouth University, Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Inria Sophia Antipolis - Méditerranée (CRISAM), University of Plymouth, and Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)

Subjects
0106 biological sciences, 0209 industrial biotechnology, chemostat, Adaptive control, Open-loop controller, Monotonic function, 02 engineering and technology, Chemostat, adaptive control, 01 natural sciences, Continuation method, 020901 industrial engineering & automation, Numerical continuation, Discrete time and continuous time, Control theory, 010608 biotechnology, Graph (abstract data type), Applied mathematics, identification, [INFO]Computer Science [cs], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH]Mathematics [math], Mathematics
Abstract

International audience; We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how to use a continuation method to reconstruct the whole graph of the growth function. Two variants, in continuous and discrete time, are presented. The case of two species in competition is also examined.

Published
2012

19. Fault diagnosis without a priori model

Author

Frédéric Hamelin, Abdouramane Moussa Ali, Cédric Join, Centre de Recherche en Automatique de Nancy (CRAN), Université Henri Poincaré - Nancy 1 (UHP)-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Algebra for Digital Identification and Estimation (ALIEN), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Centrale Lille-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Engineering, General Computer Science, free-model fault diagnosis, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Fault detection and isolation, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, Robustness (computer science), 0101 mathematics, Electrical and Electronic Engineering, Noise measurement, business.industry, Mechanical Engineering, Linear system, Fault indicator, Stuck-at fault, sensor fault, Control and Systems Engineering, actuator fault, Fault coverage, Fault model, business, Algorithm
Abstract

International audience; This article proposes an algebraic method to fault diagnosis for uncertain linear systems. The main advantage of this new approach is to realize fault diagnosis only from knowledge of input and output measurements without identifying explicitly model parameters. Using tools and results of algebraic identification and pseudospectra analysis, the issues of robustness of the pro- posed approach compared to the model order and noise measurement are examined. Numerical examples are provided and discussed to illustrate the efficiency of the proposed fault diagnosis method.

Published
2012

20. Distributed Source Identification for Wave Equations: An Offline Observer-Based Approach

Author

M. Chapouly, Mazyar Mirrahimi, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Scheme (programming language), 0209 industrial biotechnology, Iterative method, 010102 general mathematics, 02 engineering and technology, Interval (mathematics), Inverse problem, [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], Wave equation, 01 natural sciences, Computer Science Applications, Term (time), Identification (information), 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Bounded function, 0101 mathematics, Electrical and Electronic Engineering, computer, Algorithm, ComputingMilieux_MISCELLANEOUS, computer.programming_language, Mathematics
Abstract

In this paper, we consider the 1-D wave equation where the spatial domain is a bounded interval. Assuming the initial conditions to be known, we are here interested in identifying an unknown source term, while we take the Neumann derivative of the solution on one of the boundaries as the measurement output. Applying a back-and-forth iterative scheme and constructing well-chosen observers (that will be applied in an offline manner), we retrieve the source term from the measurement output in the minimal observation time.

Published
2012

21. A method for the reconstruction of unknown non-monotonic growth functions in the chemostat

Author

Serafim Rodrigues, Mathieu Desroches, Alain Rapaport, Jan Sieber, College of Engineering, Mathematics and Physical Sciences [Exeter] (EMPS), University of Exeter, Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme (MODEMIC), 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)-Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Centre for Robotics and Neural Systems (CRNS), Plymouth University, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National de la Recherche Agronomique (INRA)

Subjects
Identification, 0209 industrial biotechnology, Adaptive control, Computer science, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], Bioengineering, Monotonic function, Growth, 02 engineering and technology, Chemostat, Dynamical Systems (math.DS), Tracing, 01 natural sciences, Feedback, Slow–fast systems, 020901 industrial engineering & automation, 0103 physical sciences, FOS: Mathematics, Applied mathematics, Growth rate, Mathematics - Dynamical Systems, 010306 general physics, Numerical continuation, Competition, General Medicine, Models, Theoretical, Controllability, Graph (abstract data type), Identifiability, Biotechnology
Abstract

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out (reconstruct) the whole graph of the growth function. The process of tracing out the graph can be performed either continuously or step-wise. We present and compare both approaches. Even in the case of two species in competition, which is not directly accessible with our approach due to lack of controllability, feedback control improves identifiability of the non-dominant growth rate., Comment: expansion of ideas from proceedings paper (17 pages, 8 figures), proceedings paper is version v1

Published
2012
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22. Approximate stabilization of an infinite dimensional quantum stochastic system

Author

Pierre Rouchon, Mazyar Mirrahimi, Ram Somaraju, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
Lyapunov function, 0209 industrial biotechnology, Photon, Markov process, Expectation value, Systems and Control (eess.SY), 02 engineering and technology, Topology, infinite dimensional stochastic systems, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 03 medical and health sciences, symbols.namesake, Quantum probability, 020901 industrial engineering & automation, Fock state, Control theory, stochastic stabilization, Quantum feedback control, 0103 physical sciences, Full state feedback, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Applied mathematics, 010306 general physics, Galerkin method, Mathematics - Optimization and Control, Mathematical Physics, Microwave cavity, 030304 developmental biology, Mathematics, Probability measure, Physics, 0303 health sciences, Markov chain, Hilbert space, Statistical and Nonlinear Physics, Optimization and Control (math.OC), symbols, Computer Science - Systems and Control, Subspace topology
Abstract

We propose a feedback scheme for preparation of photon number states in a microwave cavity. Quantum Non-Demolition (QND) measurements of the cavity field and a control signal consisting of a microwave pulse injected into the cavity are used to drive the system towards a desired target photon number state. Unlike previous work, we do not use the Galerkin approximation of truncating the infinite-dimensional system Hilbert space into a finite-dimensional subspace. We use an (unbounded) strict Lyapunov function and prove that a feedback scheme that minimizes the expectation value of the Lyapunov function at each time step stabilizes the system at the desired photon number state with (a pre-specified) arbitrarily high probability. Simulations of this scheme demonstrate that we improve the performance of the controller by reducing "leakage" to high photon numbers., Comment: Submitted to CDC 2011

Published
2011

23. On stability of continuous-time quantum filters

Author

Mazyar Mirrahimi, Pierre Rouchon, Hadis Amini, Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
0209 industrial biotechnology, Generalization, Stochastic process, 010102 general mathematics, Markov process, 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Wiener process, Quantum state, Convergence (routing), Master equation, symbols, Applied mathematics, 0101 mathematics, Mathematics, Quantum computer
Abstract

International audience; We prove that the fidelity between the quantum state governed by a continuous time stochastic master equation driven by a Wiener process and its associated quantum-filter state is a sub-martingale. This result is a generalization to non-pure quantum states where fidelity does not coincide in general with a simple Frobenius inner product. This result implies the stability of such filtering process but does not necessarily ensure the asymptotic convergence of such quantum-filters.

Published
2011

24. Design of strict control-Lyapunov functions for Quantum systems with QND measurements

Author

Hadis Amini, Mazyar Mirrahimi, Pierre Rouchon, Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
Lyapunov function, 0209 industrial biotechnology, FOS: Physical sciences, Markov process, Systems and Control (eess.SY), 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Control theory, Quantum state, Computer Science::Systems and Control, 0103 physical sciences, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Statistical physics, 010306 general physics, Mathematics - Optimization and Control, Quantum, Mathematics, Quantum Physics, business.industry, Graph theory, Photon counting, Optimization and Control (math.OC), symbols, Computer Science - Systems and Control, Photonics, Quantum Physics (quant-ph), business, Laplace operator
Abstract

International audience; We consider discrete-time quantum systems subject to Quantum Non-Demolition (QND) measurements and controlled by an adjustable unitary evolution between two successive QND measures. In open-loop, such QND measurements provide a non-deterministic preparation tool exploiting the back-action of the measurement on the quantum state. We propose here a systematic method based on elementary graph theory and inversion of Laplacian matrices to construct strict control-Lyapunov functions. This yields an appropriate feedback law that stabilizes globally the system towards a chosen target state among the open-loop stable ones, and that makes in closed-loop this preparation deterministic. We illustrate such feedback laws through simulations corresponding to an experimental setup with QND photon counting.

Published
2011

25. A quadratic programming-based method for quantized system identification

Author

Xian'en Liu, Qinghua Zhang, Jiandong Wang, Peking University [Beijing], SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0209 industrial biotechnology, Mathematical optimization, Nonlinear system identification, System identification, 020206 networking & telecommunications, 02 engineering and technology, Impulse (physics), Hybrid and distributed system identification, Parameter identification problem, Nonlinear system, 020901 industrial engineering & automation, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Convex optimization, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Quadratic programming, Infinite impulse response, Mathematics
Abstract

International audience; This paper proposes a quadratic programming (QP)-based method, for linear dynamic system identification from quantized data or binary measurements. The main idea of the proposed method is to reformulate the identification problem for finite impulse (FIR) systems, usually viewed as a nonlinear estimation problem with discontinuous nonlinearities, in the form of a standard QP problem, which is a convex optimization problem and can be solved efficiently. The QP-based method is equally applicable to both quantized data and binary measurements without any modification. It has no special assumptions on the identification experiments. An iterative QP-based method is also developed for the identification of infinite impulse response (IIR) systems. Numerical examples demonstrate the effectiveness of the proposed method.

Published
2011

26. On Using Distorted Sensors for Set-Based Multi-Scale Actuator Fault Diagnosis

Author

Christophe Combastel, Qinghua Zhang, Sid-Ahmed Raka, Ecole Nationale Supérieure de l'Electronique et de ses Applications (ENSEA), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0209 industrial biotechnology, Basis (linear algebra), 020208 electrical & electronic engineering, Multiplicative function, 02 engineering and technology, Fault detection and isolation, Nonlinear system, Identification (information), Robust estimation, 020901 industrial engineering & automation, Control theory, Nonlinear distortion, Bounded function, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Diagnosis, 0202 electrical engineering, electronic engineering, information engineering, Uncertainty descriptions, Actuator, Mathematics
Abstract

International audience; The off-line fault detection, isolation and identification of multiplicative actuator faults using sensors providing measurements affected by unknown nonlinear distortions and bounded noises are addressed. The only assumption about the unknown functions modeling the sensor distortions is their monotonicity. Bounded disturbances are also considered as unknown inputs of the system time-varying dynamics. Polytopic faulty parameter sets resulting from the search of robust output pairs and from zonotope computations are the basis for a decision scheme which makes use of multi-scale temporal windows. A numerical example modeling part of a distillation column illustrates the off-line diagnosis of three multiplicative actuator faults from a single low-cost noisy sensor with unknown nonlinear distortion and constant bias.

Published
2011

27. Towards the handling of uncertaintie in statistical FDI

Author

Michèle Basseville, Qinghua Zhang, Albert Benveniste, Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-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), Distributed and Iterative Algorithms for the Management of Telecommunications Systems (DISTRIBCOM), 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)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), 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)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria Rennes – Bretagne Atlantique

Subjects
020301 aerospace & aeronautics, 0209 industrial biotechnology, Engineering, business.industry, Statistical model, 02 engineering and technology, Foreign direct investment, Fault detection and diagnosis, Fault detection and isolation, 020901 industrial engineering & automation, 0203 mechanical engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Econometrics, Statistical inference, business
Abstract

The paper provides fundamental steps towards addressing the theoretically and practically important issue of handling uncertainties in statistical model-based approaches to fault detection and isolation (FDI). Two main types of uncertainties are distinguished: uncertainties in parameters on the one hand; uncertainties due to under-modeling as well as those resulting from changes in functioning modes, on the other hand. It is suggested that two different theories should be used.

Published
2011

28. Adiabatic passage and ensemble control of quantum systems

Author

Zaki Leghtas, Alain Sarlette, Pierre Rouchon, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Electrical Engineering and Computer Science (Institut Montefiore), Université de Liège, Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
Physics, Quantum Physics, 0209 industrial biotechnology, FOS: Physical sciences, 02 engineering and technology, Condensed Matter Physics, 01 natural sciences, Atomic and Molecular Physics, and Optics, Pulse (physics), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Permutation, 020901 industrial engineering & automation, Robustness (computer science), Excited state, 0103 physical sciences, Statistical physics, Quantum Physics (quant-ph), 010306 general physics, Adiabatic process, Ground state, Quantum, Eigenvalues and eigenvectors
Abstract

This paper considers population transfer between eigenstates of a finite quantum ladder controlled by a classical electric field. Using an appropriate change of variables, we show that this setting can be set in the framework of adiabatic passage, which is known to facilitate ensemble control of quantum systems. Building on this insight, we present a mathematical proof of robustness for a control protocol -- chirped pulse -- practiced by experimentalists to drive an ensemble of quantum systems from the ground state to the most excited state. We then propose new adiabatic control protocols using a single chirped and amplitude shaped pulse, to robustly perform any permutation of eigenstate populations, on an ensemble of systems with badly known coupling strengths. Such adiabatic control protocols are illustrated by simulations achieving all 24 permutations for a 4-level ladder.

Published
2011

29. Back and forth nudging for quantum state estimation by continuous weak measurement

Author

Pierre Rouchon, Mazyar Mirrahimi, Zaki Leghtas, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
0209 industrial biotechnology, Observer (quantum physics), Estimation theory, Estimator, Observable, 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, Quantum state, 0103 physical sciences, Quantum system, Applied mathematics, Weak measurement, 010306 general physics, Mathematics, Quantum computer
Abstract

International audience; We propose to apply the Back and Forth Nudging (BFN) method used for geophysical data assimilations [1] to estimate the initial state of a quantum system. We consider a cloud of atoms interacting with a magnetic field while a single observable is being continuously measured over time using homodyne detection. The BFN method relies on designing an observer forward and backwards in time. The state of the BFN observer is continuously updated by the measured data and tends to converge to the system's state. The proposed estimator seems to be globally asymptotically convergent when the system is observable. A detailed convergence proof and simulations are given in the 2-level case. An extension of the algorithm to the multilevel case is also presented.

Published
2011

30. An adaptive observer for joint estimation of states and parameters in both state and output equations

Author

Qinghua Zhang, Xiuliang Li, Hongye Su, Zhejiang University, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Estimation, 0209 industrial biotechnology, 020208 electrical & electronic engineering, Parameterized complexity, 02 engineering and technology, State (functional analysis), Fault detection and isolation, adaptive observer, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, fault detection and isolation, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Signal Processing, Convergence (routing), 0202 electrical engineering, electronic engineering, information engineering, State observer, Electrical and Electronic Engineering, linear time-varying system, Joint (audio engineering), Alpha beta filter, Mathematics, state and parameter estimation
Abstract

An adaptive observer is a recursive algorithm for joint state–parameter estimation of parameterized state-space systems. Previous works on globally convergent adaptive observers consider unknown parameters either in state equations or in output equations, but not in both of them. In this paper, a new adaptive observer is designed for linear time-varying systems with unknown parameters in both state and output equations. Its global convergence for simultaneous estimation of states and parameters is formally established under appropriate assumptions. A numerical example is presented to illustrate the performance of this adaptive observer. Copyright © 2011 John Wiley & Sons, Ltd.

Published
2011

31. Back and forth nudging for quantum state reconstruction

Author

Ashley Donovan, Pierre Rouchon, Mazyar Mirrahimi, Department of Chemistry, Princeton University, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), ANR-09-JCJC-0070,EPOQ2,Estimation PrOblems for Quantum & Quantumlike systems(2009), and Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
0209 industrial biotechnology, Observer (quantum physics), Iterative method, Estimator, Observable, 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, Quantum state, 0103 physical sciences, Weak measurement, State observer, 010306 general physics, Quantum computer, Mathematics
Abstract

International audience; We propose an estimation method allowing to identify the initial state of a quantum system based on the continuous weak measurement of a certain physical observable over a fixed interval of time. The algorithm is based on the back- and-forth nudging method consisting in iterative application of Luenberger observers for the time-forward and time-backward dynamics. A clever change of variables unveils the needed symmetry in the observer design leading to the decrease of a certain distance (in an appropriate metric) between the estimator and the main system, both in forward and backward directions.

Published
2010

32. Stabilization of a delayed quantum system: the photon box case-study

Author

Pierre Rouchon, Mazyar Mirrahimi, Hadis Amini, Centre Automatique et Systèmes (CAS), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and MINES ParisTech - École nationale supérieure des mines de Paris

Subjects
Lyapunov function, 0209 industrial biotechnology, Stochastic process, Open-loop controller, Markov process, 02 engineering and technology, Lyapunov exponent, 01 natural sciences, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Control and Systems Engineering, Robustness (computer science), Control theory, Optimization and Control (math.OC), 0103 physical sciences, Convergence (routing), symbols, Quantum system, FOS: Mathematics, Electrical and Electronic Engineering, 010306 general physics, Mathematics - Optimization and Control, Mathematics
Abstract

We study a feedback scheme to stabilize an arbitrary photon number state in a microwave cavity. The quantum non-demolition measurement of the cavity state allows a non-deterministic preparation of Fock states. Here, by the mean of a controlled field injection, we desire to make this preparation process deterministic. The system evolves through a discrete-time Markov process and we design the feedback law applying Lyapunov techniques. Also, in our feedback design we take into account an unavoidable pure delay and we compensate it by a stochastic version of a Smith predictor. After illustrating the efficiency of the proposed feedback law through simulations, we provide a rigorous proof of the global stability of the closed-loop system based on tools from stochastic stability analysis. A brief study of the Lyapunov exponents of the linearized system around the target state gives a strong indication of the robustness of the method., Comment: submitted

Published
2010
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33. Subspace Identification Methods for Hammerstein Systems: Rank Constraint and Dimension Problem

Author

Qinghua Zhang, Chunyun Yan, Jiandong Wang, College of Engineering [Beijing], Peking University [Beijing], SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0209 industrial biotechnology, Mathematical optimization, Nonlinear system identification, Rank (linear algebra), System identification, 02 engineering and technology, Hammerstein system, Computer Science Applications, Constraint (information theory), Identification (information), 020901 industrial engineering & automation, Dimension (vector space), Control and Systems Engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, nonlinear system identification, subspace identification, Focus (optics), Subspace topology, Mathematics
Abstract

International audience; This article studies the subspace identification methods (SIMs) for Hammerstein systems with major focus on a rank constraint and the related dimension problem. We analyse the effects of the rank constraint on the three steps of a unifying framework for SIMs: the rank constraint has no effect on the first two steps, but does so on the third step. If the rank constraint is ignored, as in the existing over-parametrised method (OPM) for Hammerstein system identification, the optimality of the resulting estimate can still be established. Even so, the OPM may suffer from the dimension problem resulting in a low numerical efficiency. To resolve the dimension problem, we propose a new subspace-based method, named as the least-parametrised method (LPM), for identification of Hammerstein systems with non-coupling input nonlinearities. Simulation results are provided to demonstrate the effectiveness of the LPM, and show the necessity of considering the rank constraint to improve the numerical efficiency.

Published
2010

34. Parameter estimation of a 3-level quantum system with a single population measurement

Author

Pierre Rouchon, Mazyar Mirrahimi, Zaki Leghtas, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre Automatique et Systèmes (CAS), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), ANR-06-BLAN-0052,C-QUID,Contrôle et identification de systèmes quantiques(2006), and MINES ParisTech - École nationale supérieure des mines de Paris

Subjects
0209 industrial biotechnology, Observer (quantum physics), Field (physics), Population, FOS: Physical sciences, 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, 0103 physical sciences, Quantum system, Statistical physics, 010306 general physics, education, Physics, Quantum Physics, education.field_of_study, Observable, parameter estimation -nonlinear observers -averaging, Moment (mathematics), Nonlinear systems -quantum systems, Dipole, symbols, Quantum Physics (quant-ph), Hamiltonian (quantum mechanics)
Abstract

An observer-based Hamiltonian identification algorithm for quantum systems has been proposed recently by Bonnabel et al. The later paper provided a method to estimate the dipole moment matrix of a quantum system requiring the measurement of the populations on all states, which could be experimentally difficult to achieve. We propose here an extension to a 3-level quantum system, having access to the population of the ground state only. By more adapted choice of the control field, we will show that a continuous measurement of this observable, alone, is enough to identify the field coupling parameters (dipole moment)., submitted

Published
2009

35. Revisiting the Two-Stage Algorithm for Hammerstein system identification

Author

Lennart Ljung, Jiandong Wang, Qinghua Zhang, Peking University [Beijing], SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Linköping University (LIU)

Subjects
0209 industrial biotechnology, Mathematical optimization, Optimal estimation, System identification, Parameterized complexity, 020206 networking & telecommunications, 02 engineering and technology, Weighting, symbols.namesake, Matrix (mathematics), Nonlinear system, 020901 industrial engineering & automation, Lagrange multiplier, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, symbols, Applied mathematics, Mathematics, Complement (set theory)
Abstract

International audience; The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of block-oriented nonlinear systems including Hammerstein systems. This paper revisits an optimality result established by Bai in 1998 showing that the TSA provides the optimal estimation of a bilinearly parameterized Hammerstein system in the sense of a weighted nonlinear least-squares (LS) criterion formulated with some special weighting matrix. We will re-derive this result through the Lagrange multiplier method which is more constructive, and complement it by giving a complete parametrization of the special weighting matrices. Numerical examples of Hammerstein system identification are presented to validate the obtained theoretical results.

Published
2009

36. Diesel Particulate Filter Thermal Management Using Model-Based Design

Author

Fehd Ben-Aicha, Stephane Sadai, Karim Bencherif, Michel Sorine, RENAULT, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and SAE International

Subjects
0209 industrial biotechnology, Engineering, Diesel particulate filter, Temperature control, business.industry, Bandwidth (signal processing), Control engineering, 02 engineering and technology, Diesel fuel, 020303 mechanical engineering & transports, 020901 industrial engineering & automation, Gain scheduling, 0203 mechanical engineering, Robustness (computer science), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Model-based design, MATLAB, business, computer, computer.programming_language
Abstract

International audience; Diesel Particulate Filters (DPF) are now considered as efficient solutions to reduce Diesel PM emissions. Concerned by environment, Renault will equip all serial production Diesel vehicles with this technology. The main issue for these devices is the periodical regeneration necessary to eliminate the accumulated soot. The challenging enhancement of the regeneration event can be achieved with a better regeneration temperature control. For this purpose, a controller based on a physical model is proposed to manage the DPF temperature during active regeneration. This paper describes the methodology which has been followed to design this controller. In a first step, a reduced physical model has been developed and validated with experimental data. In a second step, two model-based controllers have been studied: a robust LPV (Linear Parameter Varying) and a gain scheduling PID..Special attention has been paid to the simplification as far as possible of the controller tuning process. Thus, the calibration parameters are only dependent upon some physical parameters and performance requirements of the closed-loop control: bandwidth, maximum overshoot. Performance robustness has been assessed in simulation. The whole modeling, controller design and validation, as well as robustness analysis have been performed using Matlab/Simulink®. Finally, the strategy has been validated on a vehicle using rapid prototyping tools.

Published
2009

37. Lyapunov control of a quantum particle in a decaying potential

Author

Mazyar Mirrahimi, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Lyapunov function, 0209 industrial biotechnology, Continuous spectrum, Free system, 02 engineering and technology, 93D15, 01 natural sciences, Schrödinger equation, symbols.namesake, Mathematics - Analysis of PDEs, 020901 industrial engineering & automation, 35Q40, Convergence (routing), FOS: Mathematics, 0101 mathematics, Mathematics - Optimization and Control, Mathematical Physics, Mathematics, Pre-compactness, Applied Mathematics, 010102 general mathematics, Spectrum (functional analysis), Mathematical analysis, Nonlinear control of PDEs, Absolute continuity, Optimization and Control (math.OC), Lyapunov techniques, symbols, Trajectory, Approximate stabilization, Dispersive estimates, Analysis, Analysis of PDEs (math.AP)
Abstract

A Lyapunov-based approach for the trajectory generation of an $N$-dimensional Schr{\"o}dinger equation in whole $\RR^N$ is proposed. For the case of a quantum particle in an $N$-dimensional decaying potential the convergence is precisely analyzed. The free system admitting a mixed spectrum, the dispersion through the absolutely continuous part is the main obstacle to ensure such a stabilization result. Whenever, the system is completely initialized in the discrete part of the spectrum, a Lyapunov strategy encoding both the distance with respect to the target state and the penalization of the passage through the continuous part of the spectrum, ensures the approximate stabilization., Comment: 34 pages

Published
2009

38. Adaptive Observers for Linear Stochastic Time-Variant Systems with Disturbances

Author

Qinghua Zhang, Stefano Perabò, 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), 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), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), 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), 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), and Université de Rennes (UNIV-RENNES)-CentraleSupélec-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique)

Subjects
0209 industrial biotechnology, Observer (quantum physics), 020208 electrical & electronic engineering, Structure (category theory), 02 engineering and technology, State (functional analysis), Fault detection and isolation, Set (abstract data type), 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Sliding window protocol, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Signal Processing, 0202 electrical engineering, electronic engineering, information engineering, A priori and a posteriori, Electrical and Electronic Engineering, Prior information, Mathematics
Abstract

Motivated by fault detection and isolation problems, we present an approach to the design of state observers for linear time-variant stochastic systems with unknown parameters and disturbances. The novelties with respect to more conventional techniques are as follows: (a) the joint estimation of state, disturbances and parameters can be carried out; (b) it is a full-stochastic approach: the unknown parameters and disturbances are random quantities and prior information, in terms of means and covariances, can be easily taken into account; (c) the observer structure is not fixed a priori, rather derived from the optimal one by means of a sliding window approximation; (d) contrary to descriptor system techniques, which estimate the state starting from a restricted set of disturbance-free equations, our approach is focused on disturbance estimation, from which state estimates are derived straightforwardly. Copyright © 2008 John Wiley & Sons, Ltd.

Published
2009

39. Observer-based Hamiltonian identification for quantum systems

Author

Mazyar Mirrahimi, Silvere Bonnabel, Pierre Rouchon, Department of Electrical Engineering and Computer Science (Institut Montefiore), Université de Liège, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), ANR-06-BLAN-0052,C-QUID,Contrôle et identification de systèmes quantiques(2006), and Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
Lyapunov function, 0209 industrial biotechnology, Adaptive control, Observer (quantum physics), Asymptotic observers, 02 engineering and technology, 01 natural sciences, Hamiltonian system, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Averaging, Control theory, 0103 physical sciences, Quantum system, Nonlinear systems, Applied mathematics, Electrical and Electronic Engineering, 010306 general physics, Mathematics, Coupling constant, System identification, Control and Systems Engineering, Qubit, Quantum systems, symbols, Symmetries
Abstract

International audience; A symmetry-preserving observer-based parameter identification algorithm for quantum systems is proposed. Starting with a 2-level quantum system (qubit), where the unknown parameters consist of the atom-laser frequency detuning and coupling constant, we prove an exponential convergence result. The analysis is inspired by Lyapunov and adaptive control techniques and is based on averaging theory. The observer is then extended to the multi-level case where all the atom-laser coupling constants are unknown. The extension of the convergence analysis is discussed through some heuristic arguments. The relevance and the robustness with respect to various noises are tested through numerical simulations.

Published
2009

40. Practical stabilization of a quantum particle in a one-dimensional infinite square potential well

Author

Mazyar Mirrahimi, Karine Beauchard, Centre de Mathématiques et de Leurs Applications (CMLA), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
bilinear Schr¨odinger equation, 0209 industrial biotechnology, Control and Optimization, Applied Mathematics, 010102 general mathematics, Mathematical analysis, control of partial differential equations, 02 engineering and technology, 01 natural sciences, Square (algebra), Schrödinger equation, symbols.namesake, 020901 industrial engineering & automation, Probability amplitude, Lyapunov stabilization, Dirichlet boundary condition, Bounded function, symbols, Quantum system, Finite potential well, quantum systems, Boundary value problem, 0101 mathematics, Mathematics
Abstract

International audience; We consider a nonrelativistic charged particle in a one-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) timedepending electric field. It is represented by a complex probability amplitude solution of a Schr¨odinger equation on a one-dimensional bounded domain, with Dirichlet boundary conditions. We prove the almost global practical stabilization of the eigenstates by explicit feedback laws.

Published
2009

41. Developments in the MathWorks System Identification Toolbox

Author

Peter Lindskog, Rajiv Singh, Anatoli Iouditski, Qinghua Zhang, Lennart Ljung, Linköping University (LIU), The MathWorks Inc., SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), NIRA Dynamics AB, Statistique et Modélisation Stochatisque (SMS), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Eric Walter, and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)

Subjects
0209 industrial biotechnology, Computer science, media_common.quotation_subject, TEKNIKVETENSKAP, 02 engineering and technology, computer.software_genre, Presentation, 020901 industrial engineering & automation, Human–computer interaction, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, TECHNOLOGY, System identification, Graphical user interface, media_common, Syntax (programming languages), Artificial neural network, Nonlinear system identification, business.industry, Programming language, 020207 software engineering, Toolbox, Look and feel, business, computer
Abstract

The paper describes additions to the System Identification Toolbox™ offered by The MathWorks, Inc, that handle the estimation of nonlinear models. Both structured grey-box models and general, flexible black-box models are covered. The idea is that the look and feel of the syntax, and the graphical user interface (GUI) should be as close as possible to the linear case. This presentation is focused on the GUI functionality and the possibilities to simulate the estimated models in Simulink™.

Published
2009

42. Convergence Speed of Unsteady Distributed Consensus: Decay Estimate Along the Settling Spanning-Trees

Author

Benedetto Piccoli, Francesco Bullo, Pierre-Alexandre Bliman, Dipartimento di Sistemi e Informatica (DSI), Università degli Studi di Firenze = University of Florence [Firenze] (UNIFI), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Università degli Studi di Firenze = University of Florence (UniFI)

Subjects
0209 industrial biotechnology, Control and Optimization, graph theory, 93C55, 02 engineering and technology, multiagent systems, distributed consensus, convergence rate, 020901 industrial engineering & automation, Consensus, Settling, 93D20, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Mathematics - Optimization and Control, Mathematics, Spanning tree, 93C05, 05C50, 05C90, 98R10, Applied Mathematics, Rate of convergence, Optimization and Control (math.OC), 020201 artificial intelligence & image processing, Algorithm
Abstract

Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries). The results appear to be tight in a number of instances and are illustrated through simple as well as more sophisticated examples. The main idea is to follow propagation of information along certain spanning trees which arise in the communication graph., 27 pages, 5 figures

Published
2009

43. Qubit Hamiltonian identification: A symmetry-preserving observer-based approach

Author

Silvere Bonnabel, Pierre Rouchon, Mazyar Mirrahimi, Department of Electrical Engineering and Computer Science (Institut Montefiore), Université de Liège, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre Automatique et Systèmes (CAS), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), ANR-06-BLAN-0052,C-QUID,Contrôle et identification de systèmes quantiques(2006), and MINES ParisTech - École nationale supérieure des mines de Paris

Subjects
Density matrix, 0209 industrial biotechnology, Observer (quantum physics), symmetries, 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Quantum system, Statistical physics, 0101 mathematics, Physics, estimation, 010102 general mathematics, General Medicine, asymptotic observers, Invariant (physics), Nonlinear system, Classical mechanics, Qubit, Homogeneous space, Quantum systems, symbols, nonlinear systems, Hamiltonian (quantum mechanics)
Abstract

International audience; We consider a pure two-state quantum system illuminated by two lasers. A photo-detector captures the fluorescence of the system. We build an invariant observer which yields a (local) estimation of the wave function (or density matrix) and the two key parameters (laser de-tuning and the atom- laser coupling strength) of the hamiltonian. The design exploits the symmetries of the system and can be interpreted geometrically. The convergence proof is based on averaging arguments. Simulation with noise illustrates the robustness of the obtained estimation algorithm.

Published
2008

44. Fault diagnosis based on the enclosure of parameters estimated with an adaptive observer

Author

Christophe Combastel, Qinghua Zhang, Abdelhalim Lalami, Equipe Commande des Systèmes (ECS), Ecole Nationale Supérieure de l'Electronique et de ses Applications, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0209 industrial biotechnology, Computer science, Computation, Adaptive system and control, Enclosure, 02 engineering and technology, General Medicine, Fault detection and diagnosis, Residual, Fault detection and isolation, Adaptive observer, 020901 industrial engineering & automation, Control theory, Robustness (computer science), Bounded function, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, False alarm, Excitation, Bounded error identification
Abstract

International audience; The proposed fault diagnosis approach associates an adaptive observer for residual generation with set-membership computations based on zonotopes for residual evaluation. The main advantage of this approach is its rigorous propagation of pre-specified modeling uncertainty bounds to the computed residuals. Within the assumed modeling uncertainty bounds, fault detection is guaranteed to be free of false alarm, while the efforts made with set-membership computation minimize the conservativeness of fault detection decisions. The novelty compared to earlier works mainly resides in a guaranteed robustness to bounded parameter variations and in a method for dealing with occasional lack of input excitation.

Published
2008

45. Real-time synchronization feedbacks for single-atom frequency standards

Author

Mazyar Mirrahimi, Pierre Rouchon, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), ANR-06-BLAN-0052,C-QUID,Contrôle et identification de systèmes quantiques(2006), and Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
0209 industrial biotechnology, quantum Monte-Carlo trajectories, Control and Optimization, Population, FOS: Physical sciences, feedback, 02 engineering and technology, 93D15, 01 natural sciences, Standard deviation, Synchronization, 34F05, 37N20, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Optical pumping, 020901 industrial engineering & automation, Control theory, 0103 physical sciences, Quantum system, 010306 general physics, education, Quantum, Mathematical Physics, Mathematics, education.field_of_study, Applied Mathematics, extremum seeking, Mathematical Physics (math-ph), Atomic clock, quantum systems, synchronization, Coherence (physics)
Abstract

Simple feedback loops, inspired from extremum-seeking, are proposed to lock a probe-frequency to the transition frequency of a single quantum system following quantum Monte-Carlo trajectories. Two specific quantum systems are addressed, a 2-level one and a 3-level one that appears in coherence population trapping and optical pumping. For both systems, the feedback algorithm is shown to be convergent in the following sense: the probe frequency converges in average towards the system-transition one and its standard deviation can be made arbitrarily small. Closed-loop simulations illustrate robustness versus jump-detection efficiency and modeling errors., 20 pages, 4 figures

Published
2008

46. Actuator Fault Diagnosis with Robustness to Sensor Distortion

Author

Qinghua Zhang, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0209 industrial biotechnology, Engineering, Article Subject, 02 engineering and technology, Hardware_PERFORMANCEANDRELIABILITY, 01 natural sciences, lcsh:QA75.5-76.95, 020901 industrial engineering & automation, Control theory, Robustness (computer science), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0103 physical sciences, Redundancy (engineering), Computer Science::Networking and Internet Architecture, Fault free, ComputerSystemsOrganization_SPECIAL-PURPOSEANDAPPLICATION-BASEDSYSTEMS, Electrical and Electronic Engineering, 010301 acoustics, business.industry, Control engineering, Soft sensor, Computer Science Applications, Actuator fault, Stuck-at fault, Nonlinear system, lcsh:TA1-2040, Modeling and Simulation, lcsh:Electronic computers. Computer science, lcsh:Engineering (General). Civil engineering (General), business, Actuator
Abstract

Actuator fault diagnosis is often studied under strong assumptions on available sensors. Typically, it is assumed that the sensors are either fault free or sufficiently redundant. The purpose of this paper is to present a new method foractuatorfault diagnosis which is robust tosensordistortion. It does not require sensor redundancy to compensate sensor distortion. The essential assumption is that sensor distortions are strictly monotonous. Despite the nonlinear and unknown nature of distortions, such sensors still provide useful information for fault diagnosis. The robustness of the presented diagnosis method is analyzed, as well as its ability to detect actuator faults. A numerical example is provided to illustrate its efficiency.

Published
2008
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47. Carbon monoxide adaptive observer for fuel cell fault detection

Author

Karim Bencherif, Qinghua Zhang, Michel Sorine, Damiano Di Penta, Technocentre Renault [Guyancourt], RENAULT, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
0209 industrial biotechnology, Materials science, Hydrogen, 020209 energy, chemistry.chemical_element, Fraction (chemistry), 02 engineering and technology, Mole fraction, 7. Clean energy, Fault detection and isolation, Fault indicator, chemistry.chemical_compound, 020901 industrial engineering & automation, chemistry, Catalytic reforming, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Transient (oscillation), Carbon monoxide
Abstract

International audience; For the purpose of fault detection in a reformate supplied fuel cell system, an adaptive observer is proposed in this paper to estimate the carbon monoxide (CO) molar fraction within the inlet gas of the fuel cell. Though CO accounts only for a small fraction in the hydrogen rich reformate, when adsorbed on the anode catalyst layer, it can considerably reduce the cell voltage, which is dangerous for the system. A high CO rate is thus an important fault indicator, however, existing sensors for CO molar fraction measurement in a gas flow are not suited to on-board applications. It is then useful to design an algorithm for its estimation from available measurements. A reduced model based on electrochemical phenomena is first briefly described and validated with experimental data. Then, we present the adaptive observer estimating the CO molar fraction, associated with a robust fault detection criterion. Finally, the algorithm is validated on transient experiments.

Published
2007

48. Robust Fault Diagnosis Based on Adaptive Estimation and Set-Membership Computations

Author

Christophe Combastel, Qinghua Zhang, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Zhang Zhang

Subjects
0209 industrial biotechnology, Computer science, zonotopes, Polytope, fault isolation, fault identification, 02 engineering and technology, Fault (power engineering), Residual, Fault detection and isolation, adaptive algorithms, 020901 industrial engineering & automation, Control theory, intervals, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, sets, Time complexity, Mathematics, observers, bounding method, General Medicine, fault diagnosis, fault detection, Bounded function, 020201 artificial intelligence & image processing, Hypercube, False alarm, Algorithm
Abstract

The proposed fault diagnosis scheme relies on a residual generation based on an adaptive observer covering linear time varying (LTV), linear parameter varying (LPV), and state-affine non-linear systems, all with bounded uncertainties. A residual evaluation is then performed by set-membership computations based on zonotopes (polytopes defined as the image of a hypercube by a linear application). The main advantage of the approach is its rigorous computation of the propagation of pre-specified modelling uncertainty bounds. Within the assumed uncertainty bounds, fault detection is guaranteed to be free of false alarm, while not being too much conservative, as illustrated on the model of a satellite. Copyright © 2006 IFAC.

Published
2007

49. Hamiltonian identification for quantum systems : well posedness and numerical approaches

Author

Claude Le Bris, Gabriel Turinici, Mazyar Mirrahimi, Herschel Rabitz, Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Methods and engineering of multiscale computing from atom to continuum (MICMAC), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Chemistry, Princeton University, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)

Subjects
0209 industrial biotechnology, Control and Optimization, Quantum dynamics, Hamiltonian identification, 02 engineering and technology, 010402 general chemistry, 01 natural sciences, Schrödinger equation, symbols.namesake, 020901 industrial engineering & automation, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum system, Uniqueness, Mathematics, Adiabatic quantum computation, 0104 chemical sciences, Computational Mathematics, Classical mechanics, Control and Systems Engineering, Quantum process, Inverse problem, symbols, optimal identification, quantum systems, Quantum algorithm, Hamiltonian (quantum mechanics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; This paper considers the inversion problem related to the manipulation of quantum systems using laser-matter interactions. The focus is on the identification of the field free Hamiltonian and/or the dipole moment of a quantum system. The evolution of the system is given by the Schrödinger equation. The available data are observations as a function of time corresponding to dynamics generated by electric fields. The well-posedness of the problem is proved, mainly focusing on the uniqueness of the solution. A numerical approach is also introduced with an illustration of its efficiency on a test problem.

Published
2007

50. Lyapunov control of bilinear Schrodinger equations

Author

Pierre Rouchon, Gabriel Turinici, Mazyar Mirrahimi, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre Automatique et Systèmes (CAS), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris Dauphine-PSL, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
TheoryofComputation_MISCELLANEOUS, Lyapunov function, 0209 industrial biotechnology, Bilinear interpolation, 02 engineering and technology, 01 natural sciences, Controllability, symbols.namesake, 020901 industrial engineering & automation, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Control and Systems Engineering, Control theory, 0103 physical sciences, Convergence (routing), Quantum system, symbols, Applied mathematics, Electrical and Electronic Engineering, 010306 general physics, Trajectory (fluid mechanics), Eigenvalues and eigenvectors, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Control-Lyapunov function, Mathematics
Abstract

International audience; A Lyapunov-based approach for trajectory tracking of the SchrÄodinger equation is proposed. In the ¯nite dimensional case, convergence is precisely analyzed. Connection between the controllability of the linear tangent approximation around the reference trajectory and asymptotic tracking is studied. When the linear tangent approximation is controllable, such a feedback ensures almost global asymptotic convergence. When the linear tangent system is not controllable, the stability of the closed- loop system is not asymptotic. To overcome such lack of convergence, we propose, when the reference trajectory is a pure-state, a modi¯cation based on adiabatic invariance. Simulations illustrate the simplicity and also the interest for trajectory generation.

Published
2005

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