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96 results on '"Aneel Tanwani"'

15. Existence and Completeness of Solutions to Extended Projected Dynamical Systems and Sector-Bounded Projection-Based Controllers

Author

W. P. M. H. Heemels, Aneel Tanwani, Eindhoven University of Technology [Eindhoven] (TU/e), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Nonsmooth dynamics, Control and Optimization, Control and Systems Engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Projection based control
Abstract

Projection-based control (PBC) systems have significant engineering impact and receive considerable scientific attention. To properly describe closed-loop PBC systems, extensions of classical projected dynamical systems are needed, because partial projection operators and irregular constraint sets (sectors) are crucial in PBC. These two features obstruct the application of existing results on existence and completeness of solutions. To establish a rigorous foundation for the analysis and design of PBC, we provide essential existence and completeness properties for this new class of discontinuous systems.

Published
2023

30. Suboptimal Filtering over Sensor Networks with Random Communication

Author

Aneel Tanwani, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Centre National de la Recherche Scientifique (CNRS), ANR-20-JSTM-0001,CyphAI,Méthodes formelles pour l'analysis et le développement de systèmes cyber-physiques intégrant l'intelligence artificielle(2020), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse 1 Capitole (UT1)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), and Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1)

Subjects
020301 aerospace & aeronautics, 0209 industrial biotechnology, Matrix differential equation, Covariance matrix, Computer science, Node (networking), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], MathematicsofComputing_NUMERICALANALYSIS, 02 engineering and technology, Covariance, Computer Science Applications, Matrix (mathematics), Filter design, 020901 industrial engineering & automation, 0203 mechanical engineering, Control and Systems Engineering, Sensor node, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, Algorithm, Wireless sensor network
Abstract

International audience; The problem of filter design is considered for linear stochastic systems using distributed sensors. Each sensor unit, represented by a node in an an undirected and connected graph, collects some information about the state and communicates its own estimate with the neighbors. It is stipulated that this communication between sensor nodes is time-sampled randomly and the sampling process is assumed to be a Poisson counter. Our proposed filtering algorithm for each sensor node is a stochastic hybrid system: It comprises a continuous-time differential equation, and at random time instants when communication takes place, each sensor node updates its state estimate based on the information received by its neighbors. In this setting, we compute the expectation of the error covariance matrix for each unit which is governed by a matrix differential equation. To study the asymptotic behavior of these covariance matrices, we show that if the gain matrices are appropriately chosen and the mean sampling rate is large enough, then the error covariances practically converge to a constant matrix.

Published
2022

33. Piecewise structure of Lyapunov functions and densely checked decrease conditions for hybrid systems

Author

Aneel Tanwani, Matteo Della Rossa, Luca Zaccarian, Rafal Goebel, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Loyola University of Chicago, University of Trento [Trento], ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Lyapunov function, 0209 industrial biotechnology, Class (set theory), Control and Optimization, Dense set, Dynamical systems theory, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Structure (category theory), Dynamical Systems (math.DS), 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, FOS: Mathematics, Applied mathematics, Mathematics - Dynamical Systems, 0101 mathematics, Mathematics, Applied Mathematics, 010102 general mathematics, Lipschitz continuity, Control and Systems Engineering, Hybrid system, Signal Processing, symbols, Piecewise
Abstract

We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a dense set and thus we avoid checking them at points of nondifferentiability of the Lyapunov function. Connections to other classes of locally Lipschitz or piecewise regular functions are also discussed and applications to hybrid dynamical systems are included., Mathematics of Control, Signals, and Systems, Springer Verlag, In press

Published
2021

34. Cone-Copositive Lyapunov Functions for Complementarity Systems: Converse Result and Polynomial Approximation

Author

Aneel Tanwani, Marianne Souaiby, Didier Henrion, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse 1 Capitole (UT1)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), and ANR-17-CE40-0019-01,ConVan,Control of Constrained Interconnected Systems Using Variational Analysis

Subjects
Lyapunov function, 0209 industrial biotechnology, Polynomial, Differential equation, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Mathematics::Optimization and Control, 02 engineering and technology, Subderivative, Rational function, 01 natural sciences, symbols.namesake, Constrained systems, 020901 industrial engineering & automation, Exponential stability, Indicator function, sums-of-squares optimization, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, FOS: Mathematics, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Applied mathematics, discretization, 0101 mathematics, Electrical and Electronic Engineering, Mathematics - Optimization and Control, Mathematics, 010102 general mathematics, converse Lyapunov theorem, hybrid systems, Computer Science Applications, Control and Systems Engineering, Optimization and Control (math.OC), symbols, Convex cone, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; This article establishes the existence of a class of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential equation coupled with a set-valued relation which introduces discontinuities in the vector field at the boundaries of the constraint set. In particular, the set-valued relation is described by the subdifferential of the indicator function of a closed convex cone, which results in a cone-complementarity system. The question of analyzing stability of such systems is addressed by constructing cone-copositive Lyapunov functions. As a first analytical result, we show that exponentially stable complementarity systems always admit a continuously differentiable cone-copositive Lyapunov function. Putting some more structure on the system vector field, such as homogeneity, we can show that the aforementioned functions can be approximated by a rational function of cone-copositive homogeneous polynomials. This later class of functions is seen to be particularly amenable for numerical computation as we provide two classes of algorithms for precisely that purpose. These algorithms consist of a hierarchy of either linear or semidefinite optimization problems for computing the desired copositive Lyapunov function. Some examples are given to illustrate our approach.

Published
2022

35. Instability of Dwell-Time Constrained Switched Nonlinear Systems

Author

Aneel Tanwani, Matteo Della Rossa, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017)

Subjects
General Computer Science, Control and Systems Engineering, Mechanical Engineering, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering
Abstract

International audience; Analyzing the stability of switched nonlinear systems under dwell-time constraints, this article investigates different scenarios where all the subsystems have a common globally asymptotically stable (GAS) equilibrium, but for the switched system, the equilibrium is not uniformly GAS for arbitrarily values of dwell-time. We motivate our study with the help of examples showing that, if near the origin all the vector fields decay at a rate slower than the linear vector fields, then the trajectories are ultimately bounded for large enough dwell-time. On the other hand, if away from the origin, the vector fields do not grow as fast as the linear vector fields, then we can only guarantee local asymptotic stability for large enough dwell-times, with region of attraction depending on the dwell-time itself. We formalize our observations for homogeneous systems, and show that, even if origin is not uniformly GAS with dwell-time switching for nonlinear systems, it still holds that the trajectories starting from a bounded set converge to a neighborhood of the origin if the dwell-time is large enough.

Published
2022

36. Nearest Neighbor Control for Practical Stabilization of Passive Nonlinear Systems

Author

Aneel Tanwani, Muhammad Zaki Almuzakki, Bayu Jayawardhana, University of Groningen [Groningen], Centre National de la Recherche Scientifique (CNRS), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Tanwani, Aneel, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Discrete Technology and Production Automation, ​Robotics and image-guided minimally-invasive surgery (ROBOTICS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
[INFO.INFO-SY] Computer Science [cs]/Systems and Control [cs.SY], 93C10, 93C30, 93C62, 93D20, output feedback, Nonlinear passive systems, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, finite control set, Optimization and Control (math.OC), Control and Systems Engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], binary control, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, Mathematics - Optimization and Control, [INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering, practical stabilization
Abstract

This paper studies static output feedback stabilization of continuous-time (incrementally) passive nonlinear systems where the control actions can only be chosen from a discrete (and possibly finite) set of points. For this purpose, we are working under the assumption that the system under consideration is large-time norm observable and the convex hull of the realizable control actions contains the target constant input (which corresponds to the equilibrium point) in its interior. We propose a nearest-neighbor based static feedback mapping from the output space to the finite set of control actions, that is able to practically stabilize the closed-loop systems. Consequently, we show that for such systems with $m$-dimensional input space, it is sufficient to have $m+1$ discrete input points (other than zero for general passive systems or the target constant input for incrementally passive systems). Furthermore, we present a constructive algorithm to design such $m+1$ nonzero input points that satisfy the conditions for practical stability using our proposed nearest-neighbor control., Comment: 13 pages, double-column, journal submission, revised version

Published
2021

37. Smooth Approximation of Patchy Lyapunov Functions for Switched Systems

Author

Luca Zaccarian, Aneel Tanwani, and Matteo Della Rossa

Subjects
Lyapunov function, 0209 industrial biotechnology, 020208 electrical & electronic engineering, 02 engineering and technology, Function (mathematics), Directional derivative, Lipschitz continuity, Stability (probability), Convolution, symbols.namesake, 020901 industrial engineering & automation, Rate of convergence, Control and Systems Engineering, Robustness (computer science), 0202 electrical engineering, electronic engineering, information engineering, symbols, Applied mathematics, Mathematics
Abstract

Starting with a locally Lipschitz (patchy) Lyapunov function for a given switched system, we provide the construction of a continuously differentiable (smooth) Lyapunov function, obtained via a convolution-based approach. This smooth function approximates the patchy function when working with Clarke's generalized gradient. The convergence rate inherited by the smooth approximations, as a by-product of our construction, is useful in establishing the robustness with respect to additive inputs. With the help of an example, we address the limitations of our approach for other notions of directional derivatives, which generally provide less conservative conditions for stability of switched systems than the conditions based on Clarke's generalized gradient.

Published
2019

38. Practical Stabilization of Passive Nonlinear Systems with Limited Control

Author

M. Muhammad Zaki Almuzakki, Aneel Tanwani, Bayu Jayawardhana, University of Groningen [Groningen], Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Discrete Technology and Production Automation, ​Robotics and image-guided minimally-invasive surgery (ROBOTICS), Tanwani, Aneel, and Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle - - ConVan2017 - ANR-17-CE40-0019 - AAPG2017 - VALID

Subjects
[INFO.INFO-SY] Computer Science [cs]/Systems and Control [cs.SY], Convex hull, 0209 industrial biotechnology, Nonlinear passive systems, Binary control, Computer science, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Space (mathematics), Finite control set, 020901 industrial engineering & automation, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Control (linguistics), Finite set, 020208 electrical & electronic engineering, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Observable, Zero (linguistics), Output feedback, Nonlinear system, Control and Systems Engineering, Norm (mathematics), Control set, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering
Abstract

International audience; This article addresses output feedback stabilization of continuous-time nonlinear systems by choosing control actions from a finite set. Working under the assumption that the system under consideration is passive and large-time norm observable, we propose a static feedback mapping, from the output space to the finite set of control actions, which is shown to be practically stabilizing if the convex hull of certain control actions (in the chosen finite set) contains the origin in its interior. Consequently, to construct this stabilizing feedback, it suffices to have, in addition to a zero symbol, another m + 1 elements in the control set which form an m-simplex in R m (the input, and output space).

Published
2019

39. ISS and integral-ISS of switched systems with nonlinear supply functions

Author

Aneel Tanwani, Shenyu Liu, Daniel Liberzon, Department of Mechanical and Aerospace Engineering [San Diego] (UCSD), University of California [San Diego] (UC San Diego), University of California-University of California, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Department of Electrical and Computer Engineering [Urbana] (University of Illinois), University of Illinois at Urbana-Champaign [Urbana], University of Illinois System-University of Illinois System, ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Department of Mechanical and Aerospace Engineering [Univ California San Diego] (MAE - UC San Diego), University of California (UC)-University of California (UC), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Department of Mechanical and Aerospace Engineering [La Jolla] (UCSD), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), and Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1)

Subjects
Lyapunov function, Bilinear systems, 0209 industrial biotechnology, Control and Optimization, Average activation time, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Input-to-state stability (ISS), 02 engineering and technology, Interval (mathematics), Stability (probability), Nonlinear stability analysis, symbols.namesake, 020901 industrial engineering & automation, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0502 economics and business, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Limit (mathematics), Switched System, Mathematics, Average dwell-time, Applied Mathematics, 05 social sciences, Dissipation inequality, Nonlinear system, Hybrid system, Integral ISS, Control and Systems Engineering, Signal Processing, symbols, 050203 business & management
Abstract

The problem of input-to-state stability (ISS) and its integral version (iISS) are considered for switched nonlinear systems with inputs, resets and possibly unstable subsystems. For the dissipation inequalities associated with the Lyapunov function of each subsystem, it is assumed that the supply functions, which characterize the decay rate and ISS/iISS gains of the subsystems, are nonlinear. The change in the value of Lyapunov functions at switching instants is described by a sum of growth and gain functions, which are also nonlinear. Using the notion of average dwell-time (ADT) to limit the number of switching instants on an interval, and the notion of average activation time (AAT) to limit the activation time for unstable systems, a formula relating ADT and AAT is derived to guarantee ISS/iISS of the switched system. Case studies of switched systems with saturating dynamics and switched bilinear systems are included for illustration of the results.

Published
2021

40. Nonpathological ISS-Lyapunov Functions for Interconnected Differential Inclusions

Author

Matteo Dellarossa, Aneel Tanwani, Luca Zaccarian, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées

Subjects
Lyapunov function, 0209 industrial biotechnology, Pure mathematics, Observer (quantum physics), Dynamical systems theory, 02 engineering and technology, Lipschitz continuity, Computer Science Applications, Nonlinear system, symbols.namesake, 020901 industrial engineering & automation, Differential inclusion, Control and Systems Engineering, Control theory, Optimization and Control (math.OC), symbols, FOS: Mathematics, Differentiable function, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, Mathematics - Optimization and Control, Mathematics
Abstract

This article concerns robustness analysis for interconnections of two dynamical systems (described by upper semicontinuous differential inclusions) using a generalized notion of derivatives associated with locally Lipschitz Lyapunov functions obtained from a finite family of differentiable functions. We first provide sufficient conditions for input-to-state stability (ISS) for differential inclusions, using a class of non-smooth (but locally Lipschitz) candidate Lyapunov functions and the concept of Lie generalized derivative. In general our conditions are less conservative than the more common Clarke derivative based conditions. We apply our result to state-dependent switched systems, and to the interconnection of two differential inclusions. As an example, we propose an observer-based controller for certain nonlinear two-mode state-dependent switched systems., Comment: IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers

Published
2021
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41. A discretization algorithm for time-varying composite gradient flow dynamics

Author

Kanat Camlibel, Aneel Tanwani, Bernoulli Institute for Mathematics and Computer Science and Artificial Intelligence, University of Groningen [Groningen], Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Systems, Control and Applied Analysis, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
0209 industrial biotechnology, Discretization, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], MathematicsofComputing_NUMERICALANALYSIS, Monotonic function, 02 engineering and technology, Maximal monotone operators, 01 natural sciences, 020901 industrial engineering & automation, Differential inclusion, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Applied mathematics, 0101 mathematics, Subgradient method, Mathematics, Gradient flow dynamics, Convex functions, 010102 general mathematics, Constrained optimization, Control and Systems Engineering, Time-stepping algorithm, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Balanced flow, Gradient descent, Convex function
Abstract

International audience; The problem of minimizing the sum, or composition, of two objective functions is a frequent sight in the field of optimization. In this article, we are interested in studying relations between the discrete-time gradient descent algorithms used for optimization of such functions and their corresponding gradient flow dynamics, when one of the functions is in particular time-dependent. It is seen that the subgradient of the underlying convex function results in differential inclusions with time-varying maximal monotone operator. We describe an algorithm for discretization of such systems which is suitable for numerical implementation. Using appropriate tools from convex and functional analysis, we study the convergence with respect to the size of the sampling interval. As an application, we study how the discretization algorithm relates to gradient descent algorithms used for constrained optimization.

Published
2020

42. Computation of Lyapunov Functions under State Constraints using Semidefinite Programming Hierarchies

Author

Didier Henrion, Marianne Souaiby, Aneel Tanwani, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J), and ANR-17-CE40-0019-01,ConVan,Control of Constrained Interconnected Systems Using Variational Analysis

Subjects
Lyapunov function, 0209 industrial biotechnology, Polynomial, convex optimization, Dynamical systems theory, Computer science, Convex set, MathematicsofComputing_NUMERICALANALYSIS, Admissible set, 02 engineering and technology, complementarity systems, symbols.namesake, Constrained systems, 020901 industrial engineering & automation, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Mathematics - Optimization and Control, Semidefinite programming, Simplex, 020208 electrical & electronic engineering, Function (mathematics), Optimization and Control (math.OC), Control and Systems Engineering, symbols, copositive Lyapunov functions, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; We provide algorithms for computing a Lyapunov function for a class of systems where the state trajectories are constrained to evolve within a closed convex set. The dynamical systems that we consider comprise a differential equation which ensures continuous evolution within the domain, and a normal cone inclusion which ensures that the state trajectory remains within a prespecified set at all times. Finding a Lyapunov function for such a system boils down to finding a function which satisfies certain inequalities on the admissible set of state constraints. It is well-known that this problem, despite being convex, is computationally difficult. For conic constraints, we provide a discretization algorithm based on simplicial partitioning of a sim-plex, so that the search of desired function is addressed by constructing a hierarchy (associated with the diameter of the cells in the partition) of linear programs. Our second algorithm is tailored to semi-algebraic sets, where a hierarchy of semidefinite programs is constructed to compute Lyapunov functions as a sum-of-squares polynomial.

Published
2020

43. Dynamical systems coupled with monotone set-valued operators: Formalisms, applications, well-posedness, and stability

Author

Aneel Tanwani, Bernard Brogliato, Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
0209 industrial biotechnology, Dynamical systems theory, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 0211 other engineering and technologies, 02 engineering and technology, complementarity systems, Maximal monotone operators, absolute stability, Theoretical Computer Science, Set-valued systems, 020901 industrial engineering & automation, Operator (computer programming), Projected dynamical system, Complementarity problems, Differential inclusion, differential inclusions, well-posedness, circuits, Lur'e systems, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Applied mathematics, normal cones, Mathematics, Lyapunov stability, 021103 operations research, piecewise linear systems, Applied Mathematics, Rotation formalisms in three dimensions, projected dynamical systems, Filippov's differential inclusions, Prox-regular sets, Computational Mathematics, Monotone polygon, Ordinary differential equation, Lagrangian systems, Passivity, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Moreau's sweeping process
Abstract

International audience; This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations (ODEs) is coupled with a static and time-varying set-valued operator in the feedback. Interconnections of this form model certain classes of nonsmooth systems including sweeping processes, differential inclusions with maximal monotone right-hand side, complementarity systems, differential and evolution variational inequalities, projected dynamical systems, some piecewise linear switching systems. Such mathematical models have seen applications in electrical circuits, mechanical systems, hysteresis effects, and many more. When we impose a passivity assumption on the open-loop system, and regard the set-valued operator in the feedback as maximally monotone, we obtain a set-valued Lur'e dynamical system. In this article we review the mathematical formalisms, their relationships, main application fields, well-posedness (existence, uniqueness, continuous dependence of solutions), and stability of equilibria. An exhaustive bibliography is provided.

Published
2020

44. Performance Bounds for Stochastic Receding Horizon Control with Randomly Sampled Measurements

Author

Lars Grüne, Debasish Chatterjee, and Aneel Tanwani

Subjects
Mathematical optimization, Model predictive control, Dynamical systems theory, Control theory, Sampling (statistics), Upper and lower bounds, Average cost, Mathematics, Standard model (cryptography), System dynamics
Abstract

This article considers the problem of analyzing the performance of model predictive controllers in minimizing infinite-horizon cost functionals associated with stochastic dynamical systems when the measurements received by the controller are randomly sampled in time. In contrast to the standard model predictive control algorithms which rely on availability of the state measurements at all times, we compute control policies which minimize cost functionals over a (finite) rolling-horizon conditioned upon the information that arrives at random time instants; although a hard upper bound equal to the length of the optimization horizon is imposed on consecutive sampling instants. Sufficient conditions are provided on the system dynamics, the cost functionals, and the statistics of the sampling process, such that the proposed policies result in computable upper bounds on the infinite-horizon average cost. The case of linear time-varying system with quadratic cost functionals is studied for the illustration of our results.

Published
2019

45. Almost Everywhere Conditions for Hybrid Lipschitz Lyapunov Functions

Author

Rafal Goebel, Matteo Della Rossa, Aneel Tanwani, Luca Zaccarian, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Loyola University of Chicago, Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018), ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Della Rossa, Matteo, Systèmes Dynamiques Hybrides et en Réseau - - HANDY2018 - ANR-18-CE40-0010 - AAPG2018 - VALID, Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle - - ConVan2017 - ANR-17-CE40-0019 - AAPG2017 - VALID, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Lyapunov function, 0209 industrial biotechnology, Dynamical systems theory, Dense set, 010102 general mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], 02 engineering and technology, Function (mathematics), Lipschitz continuity, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Exponential stability, symbols, Applied mathematics, Almost everywhere, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Differentiable function, 0101 mathematics, Mathematics
Abstract

International audience; We introduce a class of locally Lipschitz continuous functions to establish stability of hybrid dynamical systems. Under certain regularity assumptions on system dynamics, we provide sufficient conditions for asymptotic stability on the candidate Lyapunov function. In contrast to the existing literature, these conditions need to be checked only on a dense set using the conventional gradient of certain functions, without the necessity of relying on Clarke's generalized gradient. We discuss the relevance of the stated assumptions with the help of some counterexamples, underlining the subtlety of the proposed relaxation. As an application of our result, we study the stability of a classical example from the reset control literature: the Clegg integrator model, with convex and nonconvex Lyapunov functions, which are almost everywhere differentiable.

Published
2019

46. Convergence of proximal solutions for evolution inclusions with time-dependent maximal monotone operators

Author

Luigi Iannelli, Aneel Tanwani, Kanat Camlibel, Johann Bernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence, University of Groningen [Groningen], University of Bennevento, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Systems, Control and Applied Analysis, Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
0209 industrial biotechnology, Sequence, 021103 operations research, Discretization, Differential equation, General Mathematics, Numerical analysis, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 0211 other engineering and technologies, Monotonic function, 02 engineering and technology, 34A60 90C33, 020901 industrial engineering & automation, Monotone polygon, Operator (computer programming), Differential inclusion, Optimization and Control (math.OC), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, FOS: Mathematics, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control, Software, Mathematics
Abstract

This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping having the property that, for a given time instant, the set-valued mapping describes a maximal monotone operator. Under certain mild assumptions on the regularity with respect to the time argument, we construct a sequence of functions parameterized by the sampling time that corresponds to the discretization of the continuous-time system. Using appropriate tools from functional and variational analysis, this sequence is then shown to converge to the unique solution of the original differential inclusion. The result is applied to develop conditions for well-posedness of differential equations interconnected with nonsmooth time-dependent complementarity relations, using passivity of underlying dynamics (equivalently expressed in terms of linear matrix inequalities)., Comment: Accepted for publication in Mathematical Programming. The first version of this manuscript was submitted on arXiv with a different title: "Evolution inclusions with time-dependent maximal monotone operators."

Published
2019

47. Detectability and Observer Design for Switched Differential Algebraic Equations

Author

Stephan Trenn, Aneel Tanwani, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Department of Mathematics (University of Groningen), University of Groningen [Groningen], ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Systems, Control and Applied Analysis, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
0209 industrial biotechnology, Observer (quantum physics), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Systems and Control (eess.SY), Dynamical Systems (math.DS), 02 engineering and technology, Interval (mathematics), Asymptotic convergence, 020901 industrial engineering & automation, TO-STATE STABILITY, Exponential stability, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, 0202 electrical engineering, electronic engineering, information engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Observer design, Applied mathematics, Observability, Electrical and Electronic Engineering, Differential–algebraic equations, Mathematics - Dynamical Systems, Mathematics - Optimization and Control, Switched systems, Mathematics, 020208 electrical & electronic engineering, Estimator, Observable, State (functional analysis), Detectability, Optimization and Control (math.OC), Control and Systems Engineering, Computer Science - Systems and Control, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Differential algebraic equation, State estimation
Abstract

International audience; This paper studies detectability for switched linear differential–algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor at the end of that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component of the system is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption.

Published
2019

48. ISS Lyapunov Functions for Cascade Switched Systems and Sampled-Data Control

Author

GuangXue Zhang and Aneel Tanwani

Subjects
Lyapunov function, 0209 industrial biotechnology, Observer (quantum physics), Computer science, 02 engineering and technology, Systems and Control (eess.SY), Dynamical Systems (math.DS), Stability (probability), Electrical Engineering and Systems Science - Systems and Control, symbols.namesake, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Electrical and Electronic Engineering, Mathematics - Dynamical Systems, Mathematics - Optimization and Control, 020208 electrical & electronic engineering, Function (mathematics), Nonlinear system, Control and Systems Engineering, Cascade, Optimization and Control (math.OC), Hybrid system, Bounded function, symbols
Abstract

Input-to-state stability (ISS) of switched systems is studied where the individual subsystems are connected in a serial cascade configuration, and the states are allowed to reset at switching times. An ISS Lyapunov function is associated to each of the two blocks connected in cascade, and these functions are used as building blocks for constructing ISS Lyapunov function for the interconnected system. The derivative of individual Lyapunov functions may be bounded by nonlinear decay functions, and the growth in the value of Lyapunov function at switching times may also be a nonlinear function of the value of other Lyapunov functions. The stability of overall hybrid system is analyzed by constructing a newly constructed ISS-Lyapunov function and deriving lower bounds on the average dwell-time. The particular case of linear subsystems and quadratic Lyapunov functions is also studied. The tools are also used for studying the observer-based feedback stabilization of a nonlinear switched system with event-based sampling of the output and control inputs. We design dynamic sampling algorithms based on the proposed Lyapunov functions and analyze the stability of the resulting closed-loop system., Comment: The article has been published in Automatica. Minor corrections/modifications compared to the journal version are indicated in blue colored text

Published
2019
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49. Max-Min Lyapunov Functions for Switching Differential Inclusions

Author

Luca Zaccarian, Matteo Della Rossa, Aneel Tanwani, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Convex hull, Lyapunov function, 0209 industrial biotechnology, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Linear system, 010103 numerical & computational mathematics, 02 engineering and technology, Positive-definite matrix, Function (mathematics), Lipschitz continuity, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Differential inclusion, symbols, Applied mathematics, Vector field, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Mathematics
Abstract

International audience; We use a class of locally Lipschitz continuous Lyapunov functions to establish stability for a class of differential inclusions where the set-valued map on the right-hand-side comprises the convex hull of a finite number of vector fields. Starting with a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations over this family of functions is a Lyapunov function for the system under consideration. For the case of linear systems, using the S-Procedure, our conditions result in bilinear matrix inequalities. The proposed construction also provides nonconvex Lyapunov functions, which are shown to be useful for systems with state-dependent switching that do not admit a convex Lyapunov function.

Published
2018

50. Error covariance bounds for suboptimal filters with Lipschitzian drift and Poisson-sampled measurements

Author

Olga O. Yufereva, Aneel Tanwani, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Krasovskii Institute of Mathematics and Mechanics, URAL Branch of RAS, ANR-17-CE40-0019,ConVan,Contrôle des Systèmes Interconnectés sous Contraintes en Utilisant l'Analyse Variationelle(2017), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
0209 industrial biotechnology, Differential equation, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 020208 electrical & electronic engineering, 02 engineering and technology, Filter (signal processing), Covariance, Expected value, Dynamical system, Poisson distribution, Nonlinear system, symbols.namesake, 020901 industrial engineering & automation, Control and Systems Engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], 0202 electrical engineering, electronic engineering, information engineering, symbols, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, Linear filter, Mathematics
Abstract

International audience; We design suboptimal filters for a class of continuous-time nonlinear stochastic systems when the measurements are assumed to arrive randomly at discrete times under a Poisson distribution. The proposed filter is a dynamical system with a differential equation and a reset map which updates the estimate whenever a new measurement is received. We analyze the performance of the proposed filter by computing the expected value of the error covariance which is described by a differential equation. We study throughly the conditions under which the error covariance remains bounded, which depend on the system data and the mean sampling rate associated with the measurement process. We also study the particular cases when the error covariance is seen to decrease with the increase in the sampling rate. For the particular case of linear filters, we can also compare the error covariance bounds with the case when the measurements are continuously available.

Published
2020

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