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Many control algorithms for ABS systems have been proposed in the literature since the introduction of this equipment by Bosch in 1978. In general, one can divide these control algorithms into two different types: those based on a regulation logic with wheel acceleration thresholds that are used by most commercial ABS systems; and those based on wheel slip control that are preferred in the large majority of academic algorithms. Each approach has its pros and cons [Shida 2010]. Oversimplifying, one can say that the strength of the first ones is their robustness; while that of the latter ones their short braking distances (on dry grounds) and their absence of limit cycles. At the midpoint of this industry/academy dichotomy, based on the concept of extended braking stiffness (XBS), a quite different class of ABS control strategies has been proposed by several researchers (see, e.g., [Sugai 1999] and [Ono 2003]). This concept combines the advantages from both the industrial and academic approaches. Nevertheless, since the slope of the tyre characteristic is not directly measurable, it introduces the question of real-time XBS estimation. The first part of this thesis is devoted to the study of this estimation problem and to a generalization of the proposed technique to a larger class of systems. From the technological point of view, the design of ABS control systems is highly dependent on the ABS system characteristics and actuator performance. Current ABS control algorithms on passenger cars, for instance the Bosch ABS algorithm, are based on heuristics that are deeply associated to the hydraulic nature of the actuator. An interesting observation is that they seem to work properly only in the presence of a specific delay coming from the hydraulic actuation [Gerard 2012]. For brake systems that have different delays compared to those of hydraulic actuators, like electric in-wheel motors (with a smaller delay) or pneumatic trailer brakes (with a bigger delay), they might be no longer suitable [Miller 2013]. Therefore, adapting standard ABS algorithms to other advanced actuators becomes an imperative goal in the automobile industry. This goal can be reached by the compensation of the delays induced by actuators. The second part of this thesis is focused on this issue, and to the generalization of the proposed technique to a particular class of nonlinear systems. Throughout this thesis, we employ two different linearization techniques: the linearization of the error dynamics in the construction of model-based observers [Krener 1983] and the linearization based on restricted state feedback [Brockett 1979]. The former is one of the simplest ways to build an observer for dynamical systems with output and to analyze its convergence. The main idea is to transform the original nonlinear system via a coordinate change to a special form that admits an observer with a linear error dynamics and thus the observer gains can be easily computed to ensure the observer convergence. The latter is a classical method to control nonlinear systems by converting them into a controllable linear state equation via the cancellation of their nonlinearities. It is worth mentioning that existing results for observer design by error linearization in the literature are only applied to the case of regular time scalings ([Guay 2002] and [Respondek 2004]). The thesis shows how to extend them to the case of singular time scalings. Besides, the thesis combines the classical state feedback linearization with a new method for the input delay compensation to resolve the output tracking problem for restricted feedback linearizable systems with input delays.; Depuis l'introduction du premier système ABS par Bosch, en 1978, de nombreux algorithmes de commande pour les systèmes ABS ont été proposés dans la littérature. En général, ces algorithmes peuvent être divisés en deux catégories : ceux basés sur une logique de régulation déterminée par des seuils sur l'accélération angulaire des roues et ceux basés sur la régulation du taux de glissement. Chaque approche a ses avantages et ses inconvénients. D'une manière simplifiée, on peut dire que le point fort du premier type est sa robustesse ; tandis que ceux du deuxième type sont leur courte distance de freinage (sur les terrains secs) et leur absence de cycles limite. Au milieu de cette dichotomie industrielle/académique, en se basant sur un concept appelé extended braking stiffness (XBS), une classe complètement différente de stratégies de commande pour l'ABS a été proposée par certains chercheurs. Ce concept combine les avantages des deux approches. Néanmoins, puisque l’XBS n'est pas directement mesurable, elle introduit la question de son estimation en temps réel. La première partie de cette thèse est consacrée à l'étude de ce problème d'estimation et à une généralisation de la technique proposée à une plus grande classe de systèmes. D'un point de vue technologique, la conception des systèmes de contrôle pour l'ABS est fortement dépendante des caractéristiques physiques du système et des performances de l'actionneur. Les algorithmes de commande actuels pour l'ABS sur les véhicules, par exemple l'algorithme ABS de Bosch, sont basés sur des approches heuristiques qui sont profondément liées à la nature hydraulique de l'actionneur. Ils ne fonctionnent correctement qu'en présence d'un retard spécifique associé à la nature hydraulique de l'actionneur. Pour les systèmes de freinage qui ont un retard différent de ceux des actionneurs hydrauliques, comme les moteurs-roues électriques par exemple (un retard plus court) ou les freins pneumatiques des semi-remorques (un retard plus grand), ils ne sont plus appropriés et ont un fonctionnement déficient. Par conséquent, l'adaptation des algorithmes standards de l'ABS pour d'autres actionneurs avancés devient un objectif primordial dans l'industrie automobile. Cet objectif peut être atteint par la compensation des retards induits par les actionneurs. La deuxième partie de cette thèse se concentre sur cette question, et à la généralisation de la technique proposée à une classe particulière de systèmes non linéaires.Tout au long de cette thèse, nous utilisons deux techniques de linéarisation différentes : la linéarisation de la dynamique d'erreur dans la construction des observateurs basés sur des modèles et la linéarisation basée sur le retour d'état restreint. La première est l'une des façons les plus simples pour synthétiser un observateur pour des systèmes dynamiques avec sortie et pour analyser sa convergence. L'idée principale est de transformer le système non linéaire original via un changement de coordonnées en un système différemment formalisé, qui admette un observateur avec une dynamique d'erreur linéaire et les gains de l'observateur peuvent donc être facilement calculés pour en assurer la convergence. Cette dernière est une méthode classique pour commander des systèmes non linéaires en les convertissant en une équation d'état linéaire contrôlable via l'annulation de leurs non-linéarités. Il convient de mentionner que les résultats existants pour la synthèse des observateurs par la linéarisation de l'erreur dans la littérature ne sont appliqués que pour le cas des changements réguliers de l'échelle de temps. Cette thèse explique comment les étendre aux cas des changements singuliers de l'échelle de temps. Par ailleurs, la thèse combine la linéarisation classique par retour d'état avec une nouvelle méthode de compensation du retard de l'entrée pour résoudre le problème de suivi de la sortie pour des systèmes linéarisables par retour d'état restreint avec des retards de l'entrée.

This paper proposes a switching steering vehicle control designed using the linear quadratic regulator (LQR) problem, the Linear Matrix Inequality (LMI) framework and the H norm. The proposed switched control law comprises two levels: the first level is a switched Proportional-Integral-Derivative controller of lateral deviation (PIDy) and the second is a switched Proportional-Derivative controller of yaw angle (PDÈ). These two levels are used to ensure an accurate tracking of the vehicle's lateral deviation y and yaw angle È. This control strategy makes use of a common Lyapunov function design method used for the stability analysis of switched continuous-time systems. Sufficient conditions for global convergence of the switched control law are presented and proved under arbitrary switching signals. All these conditions are expressed in terms of LMIs. The switched steering control was developed for an application seeking to identify approximately the maximum achievable speed in a bend. This application requires a steering control for simulating a realistic nonlinear four-wheel vehicle model and for performing a speed extrapolation test to evaluate the physical limits of a vehicle in a bend. This study includes the performance tests using experimental data from the Peugeot 307 prototype vehicle developed by IFSTTAR Laboratory.

It is well known that the stability analysis of step-by-step numerical methods for differential equations often reduces to the analysis of linear difference equations with variable coefficients. This class of difference equations leads to a family \(\mathcal{F}\) of matrices depending on some parameters and the behaviour of the solutions depends on the convergence properties of the products of the matrices of \(\mathcal{F}\). To date, the techniques mainly used in the literature are confined to the search for a suitable norm and for conditions on the parameters such that the matrices of \(\mathcal{F}\) are contractive in that norm. In general, the resulting conditions are more restrictive than necessary. An alternative and more effective approach is based on the concept of joint spectral radius of the family \(\mathcal{F}\), \(\rho (\mathcal{F})\). It is known that all the products of matrices of \(\mathcal{F}\) asymptotically vanish if and only if \(\rho (\mathcal{F}) < 1\). The aim of this chapter is that to discuss the main theoretical and computational aspects involved in the analysis of the joint spectral radius and in applying this tool to the stability analysis of the discretizations of differential equations as well as to other stability problems. In particular, in the last section, we present some recent heuristic techniques for the search of optimal products in finite families, which constitutes a fundamental step in the algorithms which we discuss. The material we present in the final section is part of an original research which is in progress and is still unpublished.

We focus on the simulation of periodically switched linear circuits. The basic notation and theoretical framework are presented, with emphasis on the differences between the linear time-invariant and the time-varying cases. For this important class of circuits and sources defined by periodic signals, the computation of their steady-state response is carried out via the solution of an augmented time-invariant MNA equation in the frequency-domain. The proposed method is based on the expansion of the unknown voltages and currents in terms of Fourier series and on the automatic generation of augmented equivalents of the circuit components. The above equivalents along with the information on circuit topology allow creating, via circuit inspection, a time-invariant MNA equation, the solution of which provides the coefficients of both the time- and the frequency-domain responses of the circuit. Analytical and numerical examples are used to stress the generality and benefits of the proposed approach.

International audience; This paper deals with switched linear system identification and more particularly aims at solving switched linear regression problems in a large-scale setting with both numerous data and many parameters to learn. We consider the recent minimum-of-error framework with a quadratic loss function, in which an objective function based on a sum of minimum errors with respect to multiple submodels is to be minimized. The paper proposes a new approach to the optimization of this nonsmooth and nonconvex objective function, which relies on Difference of Convex (DC) functions programming. In particular, we formulate a proper DC decomposition of the objective function, which allows us to derive a computationally efficient DC algorithm. Numerical experiments show that the method can efficiently and accurately learn switching models in large dimensions and from many data points.

This thesis is dedicated to the control and the observation of a class of switched linear systems (SLS). This class contains the systems that can be represented by a port-Hamiltonian model. A lot of works have been studied SLS for several years using an average modeling approach. Recently, various works have shown that hybrid system theory allows to cope with stabilization, controllability, and observability problems of switched linear systems. However, several problems are still open and need more development such as the design of hybrid observers for SLS that have unobservable modes or the control of systems with reduced number of switching inputs and numerous variable states to control. In this work, we are interested in the design of state observers for a particular class of SLS using both the average and the hybrid port-Hamiltonian models. This formalism has the necessary tools to study and establish the stability of the observation errors. At the beginning, a nonlinear observer based on the average modeling is proposed. Next, a hybrid observer is designed for switched linear systems. This observer takes into account the unobservable operating modes of the system. The second point of our work concerns the design of control laws for the considered class of SLS. At first, two Lyapunov-based control laws have been established using either an average model or a hybrid model of the system. A hybrid optimal control based on the maximum principle of Pontryagin and the computation of singular arcs has been also proposed. Finally, a hybrid predictive control based on a discrete model of the system is synthesized. Simulation results and an experimental implementation on a SEPIC converter are given to show the efficiency of the proposed methods. Our motivation to study such a converter is mainly due to its particular topology that includes observable and unobservable subsystems. It is also known to be difficult to be controlled because only one switching input is used to control four state variables., Cette thèse s’intéresse à la commande et l’observation d’une classe de systèmes linéaires à commutations (SLC). La classe considérée regroupe les systèmes pouvant être représentés par un modèle Hamiltonien à ports. Récemment, plusieurs travaux ont utilisé la théorie des systèmes dynamiques hybrides pour traiter les problèmes de stabilité, de commandabilité et d’observabilité des systèmes linéaires à commutations. Cependant, certains verrous scientifiques demeurent et nécessitent d’être levés tels que la synthèse d’observateurs pour des SLC présentant des modes de fonctionnement inobservables ou la commande hybride de systèmes possédant un nombre réduit d’entrées de commutations et un nombre élevé de variables d’état à contrôler. Dans ce travail, nous nous intéressons à la synthèse d’observateurs s’appuyant sur la modélisation moyenne et la modélisation hybride de SLC ayant une topologie Hamiltonienne à ports particulière. Ce formalisme possède les outils nécessaires pour établir des preuves de stabilité des erreurs d’observation. Dans un premier temps, nous proposons un observateur non linéaire reposant sur le modèle moyen de la classe des SLC considérée. Ensuite, nous traitons le problème de synthèse d’un observateur hybride où nous proposons un observateur commuté prenant en compte les modes de fonctionnement inobservables. Le problème de la commande des SLC est abordé par la suite. Au départ, la théorie de Lyapunov est utilisée pour proposer deux lois de commandes : La première est synthétisée à partir du modèle moyen et la deuxième exploite le modèle hybride. Une commande optimale hybride est élaborée en utilisant le principe du maximum de Pontryagin et une approche utilisant la recherche d’arcs singuliers. Finalement, une commande prédictive hybride est établie à partir d’un modèle discrétisé du système. Des résultats de simulation et une mise en œuvre expérimentale sur un convertisseur DC-DC SEPIC sont donnés pour montrer l’efficacité des méthodes proposées. L’étude d’un tel circuit est motivée par sa topologie particulière qui contient à la fois un mode de fonctionnement observable et un mode de fonctionnement inobservable. En outre, il possède une seule entrée de commutations et quatre variables d’état ce qui lui vaut la réputation être difficile à commander.

This paper proposes a general convex framework for the identification of switched linear systems. The proposed framework uses over-parameterization to avoid solving the otherwise combinatorially forbidding identification problem, and takes the form of a least-squares problem with a sum-of-norms regularization, a generalization of the ℓ1-regularization. The regularization constant regulates the complexity and is used to trade off the fit and the number of submodels. Funding Agencies|Swedish foundation for strategic research in the center MOVIII||Swedish Research Council in the Linnaeus center CADICS||European Research Council|267381|Sweden-America Foundation||Swedish Science Foundation

Wind turbines are being used to generate electricity as an alternative energy source to conventional fossil fu- els, and it is well known that wind towers must to sus- tain continuous vibration forces throughout their opera- tional life. In this paper, a stability analysis of bending deflection of a wind turbine steel tower is presented. The wind turbine is modelled as the structure of a sim- plified beam-column by a switched system. It is mod- elled by using a Hamiltonian system, which simplifies the system under study and allows to analyze the sta- bility dynamics of the system. An eigenvalue analysis have been done in order to analyze the stability of the system; finally, also, some transient simulations of the system are presented to verify the results obtained

In this note we prove that if a switched system F formed by a pair of linear vector fields of R 2 is asymptotically controllable, then the discrete time operator associated to F admits at least one real eigenvalue λ, with |λ

This work deals with rejection of inaccessible signals in discrete-time linear switching systems, with the requirement that the compensated system be quadratically stable under arbitrary switching. A constructive condition is provided for devising a switching state feedback achieving zero output for any admissible inaccessible input sequence and any initial state in a certain subspace, while attaining quadratic stability under arbitrary switching of the closed-loop dynamics. The constructive condition is twofold, since structural and stability issues are considered independently of each others. The methodological bases consist of both classic and novel ideas of the geometric approach, enhanced with the notion of quadratic stability under arbitrary switching. The theoretical results are supported by a complete computational framework, developed in Matlab by using the algorithms of the geometric approach and the LMI solvers.

International audience; This paper deals with Networked Control Systems (NCS) design, under the constraint of limited bandwidth on the communication channel. A linear quadratic regulator for a fixed sampling period is solved and this result is used for the development of H2 and Hoo performance indexes, yielding to the statement and solution of H2 and Hoo optimal control problems. Finally, a self-triggered controller is designed with a switched system approach in order to improve performance. Examples are presented in order to illustrate the validity of the theory.

15th International Congress on Computational and Applied Mathematics (ICCAM) -- JUL 05-09, 2010 -- Univ Leuven, Leuven, BELGIUM, WOS: 000305360000012, Consider the stability problem for the following linear switched system (differential inclusion) (x) over dot = Ax, A is an element of {A1, A2, . . . , A(N)}. Here A(i) (i = 1, 2, . . . . N) are n x n dimensional Hurwitz stable real matrices. In this study for this system we investigate the problem of the existence and construction of a common diagonal Lyapunov function of the form V(x) = x(T) Dx where D is a positive diagonal matrix. In the case of n = 3, i.e. third order system, we suggest a simple elimination algorithm which gives a common Din the case of existence, Ghent Univ, Fac Sci

International audience; This paper addresses the problem of flat output characterization for switched linear systems along with an extension to LPV systems. A condition which has a polynomial complexity with respect to the dimension of the system and a practical approach for checking this condition are provided.

In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average dwell time (MDADT) are investigated in both continuous-time and discrete-time contexts. The proposed switching law is more applicable in practice than the average dwell time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques. Refereed/Peer-reviewed

In this paper, we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version, the exogenous input is considered as the disturbance, in the second, the switching signal and in the third both of them are considered as disturbances. All three versions of disturbance decoupling have direct counterparts for linear parameter-varying (LPV) systems, while the latter instance of the problem is relevant for disturbance decoupling of piecewise linear systems, as we will show. The solutions of the three disturbance decoupling problems will be based on geometric control theory for switched linear systems and will entail both mode-dependent and mode-independent static state feedback.

This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results., {"references":["V.N. Phat and P.T. Nam (2007), Exponential stability and stabilization\nof uncertain linear time-varying systems using parameter dependent\nLyapunov function. Int. J. of Control, 80, 1333-1341.","V.N. Phat and P. Niamsup, Stability analysis for a class of functional differential\nequations and applications. Nonlinear Analysis: Theory, Methods\n& Applications 71(2009), 6265-6275.","V.N. Phat, T. Bormat and P. Niamsup, Switching design for exponential\nstability of a class of nonlinear hybrid time-delay systems, Nonlinear\nAnalysis: Hybrid Systems, 3(2009), 1-10.","Y.J. Sun, Global stabilizability of uncertain systems with time-varying\ndelays via dynamic observer-based output feedback, Linear Algebra and\nits Applications, 353(2002), 91-105.","O.M. Kwon and J.H. Park, Delay-range-dependent stabilization of uncertain\ndynamic systems with interval time-varying delays, Applied Math.\nConputation, 208(2009), 58-68.","H. Shao, New delay-dependent stability criteria for systems with interval\ndelay, Automatica, 45(2009), 744-749.","J. Sun, G.P. Liu, J. Chen and D. Rees, Improved delay-range-dependent\nstability criteria for linear systems with time-varying delays, Automatica,\n46(2010), 466-470.","W. Zhang, X. Cai and Z. Han, Robust stability criteria for systems with\ninterval time-varying delay and nonlinear perturbations, J. Comput. Appl.\nMath., 234 (2010), 174-180.","V.N. Phat, Robust stability and stabilizability of uncertain linear hybrid\nsystems with state delays, IEEE Trans. CAS II, 52(2005), 94-98.\n[10] V.N. Phat and P.T. Nam (2007), Exponential stability and stabilization\nof uncertain linear time-varying systems using parameter dependent\nLyapunov function. Int. J. of Control, 80, 1333-1341.\n[11] V.N. Phat and P. Niamsup, Stability analysis for a class of functional differential\nequations and applications. Nonlinear Analysis: Theory, Methods\n& Applications 71(2009), 6265-6275.\n[12] V.N. Phat and P.T. Nam (2007), Exponential stability and stabilization\nof uncertain linear time-varying systems using parameter dependent\nLyapunov function. Int. J. of Control, 80, 1333-1341.\n[13] V.N. Phat and P. Niamsup, Stability analysis for a class of functional differential\nequations and applications. Nonlinear Analysis: Theory, Methods\n& Applications 71(2009), 6265-6275.\n[14] V.N. Phat, Y. Khongtham, and K. Ratchagit, LMI approach to exponential\nstability of linear systems with interval time-varying delays. Linear\nAlgebra and its Applications 436(2012), 243-251.\n[15] K. Ratchagit and V.N. Phat, Stability criterion for discrete-time systems,\nJ. Ineq. Appl., 2010(2010), 1-6.\n[16] F. Uhlig, A recurring theorem about pairs of quadratic forms and\nextensions, Linear Algebra Appl., 25(1979), 219-237.\n[17] K. Gu, An integral inequality in the stability problem of time delay\nsystems, in: IEEE Control Systems Society and Proceedings of IEEE\nConference on Decision and Control, IEEE Publisher, New York, 2000.\n[18] Y. Wang, L. Xie and C.E. de SOUZA, Robust control of a class of\nuncertain nonlinear systems. Syst. Control Lett., 1991992), 139-149.\n[19] S. Boyd, L.El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix\nInequalities in System and Control Theory, SIAM, Philadelphia, 1994.\n[20] J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential\nEquations, Springer-Verlag, New York, 1993."]}

International audience; This paper is devoted to dynamic output feedback View the MathML source control design of switched linear systems in both continuous and discrete-time domains. More specifically, the main purpose is to jointly design a switching rule and a full order dynamic output feedback switched controller that render the associated closed-loop switched linear system globally asymptotically stable and impose a pre-specified upper bound to the View the MathML source gain. An example of practical importance is presented to illustrate the validity and efficiency of the theory.

International audience; The work presented in this paper is concerned with the identification of switched linear systems from input-output data. The main challenge with this problem is that the data are available only as a mixture of observations generated by a finite set of different interacting linear subsystems so that one does not know a priori which subsystem has generated which data. To overcome this difficulty, we present here a sparse optimization approach inspired by very recent developments from the community of compressed sensing. We formally pose the problem of identifying each submodel as a combinatorial $\ell_0$ optimization problem. This is indeed an NP-hard problem which can interestingly, as shown by recent literature, be relaxed into a (convex) $\ell_1$-norm minimization problem. We present sufficient conditions for this relaxation to be exact. The whole identification procedure allows us to extract the parameter vectors (associated with the different subsystems) one after another without any prior clustering of the data according to their respective generating-submodels. Some simulation results are included to support the potentialities of the proposed method.

This document synthesizes my Phd thesis work in Automatic Control in Grenoble-INP. This thesis has been prepared in the automatic control department of thelaboratory GIPSA-lab. This work is situated in the area of traffic systems control andsupervision. Our contributions are about modeling, supervision and local traffic control.The CTM traffic model has been extended with a model of uncertainties. Thisnews model allows us to take into account the uncertain parameters of the model, topropose new robust switched control law.In addition to this modeling approach, we propose some developments on supervisionof trafic systems. On one hand, we can estimate the operating mode of thesystem in real time and on the other hand to estimate some faults on the system. Thedynamical estimation of the operating mode allows us to know the state of congestion(or non congestion) of the road. We are able to estimate faults such as speed fall andcapacities drop that may appear.Finally, we propose two control laws based on switching systems control. The developedcontrollers adapt their geometry to the properties of the system. The purposeof these controllers is to be inserted in a hierarchic control scheme., Ce document synthétise mes travaux de thèse de doctorat en Automatique Productiqueà Grenoble INP (Institut National Polytechnique), thèse préparée au sein dudépartement automatique du laboratoire GIPSA-lab (Grenoble Image Parole Signal etAutomatique). Ce travail s’inscrit dans le cadre du contrôle local et de la supervisiondes systèmes de trafic routier. Les principales contributions portent sur la modélisation,la supervision et la commande locale des systèmes de trafic routier.La contribution apportée à la modélisation du trafic est l’ajout d’un modèle d’incertitudesur le modèle CTM (Cell Transmission Model [Daganzo, 1994]). Ce nouveaumodèle permet de prendre en compte les incertitudes sur différents paramètres dumodèle pour in-fine proposer de nouvelles stratégies de commandes commutées robustes.Outre cette approche de modélisation, nous proposons un niveau de supervisionpermettant d’une part d’estimer en temps réel le mode de fonctionnement et d’autrepart de détecter, localiser et estimer certaines fautes sur le système. L’estimation dynamiquede mode de fonctionnement nous permet de connaître l’état de congestion (ou denon-congestion) de l’aménagement routier considéré. Nous sommes en mesure de détecterdes fautes telles que des chutes de vitesse ou des chutes de capacité survenant sur la route.Enfin, nous proposons deux lois de commandes locales basées sur la théorie dessystèmes à commutations. Ainsi, le schéma de contrôle s’adaptera dynamiquementaux changements de propriétés du système. Ces lois de commande ont pour objet des’insérer dans un schéma de régulation hiérarchique.

This PhD thesis is dedicated to the synthesis of the state estimation in a finite time by an algebraic approach (the techniques developed within the ALIEN group) for the linear time-invariant systems (LTI) subject to the external unknown disturbances, the linear time-varying systems (LTV) and the switched linear systems (SLC) in continuous time. For the LTI and LTV systems, a formal expression of state as a function of iterated integrals of the output and the input is obtained. For switched linear systems, combining the results of state estimation for LTI systems and switch instant detection presented in Chapter 4, we give the main approach of current mode estimation and the continuous state estimation in real time. To do this, one applies some mathematical tools: Laplace transforms, the operational calculus and the theory of distribution; Ce mémoire est dédié à l’étude de la synthèse de l’estimation d’état en temps fini par une approche algébrique (les techniques développées au sein de l’équipe ALIEN) pour les systèmes linéaires à paramètres invariant dans le temps (LTI) sujets à des perturbations extérieures inconnues, les systèmes linéaires à paramètres variant dans le temps (LTV) et les systèmes linéaires à commutation en temps continu (SLC). Pour les systèmes LTI et LTV, une expression formelle de l’état en fonction des intégrales itérées des sorties et de l’entrée a été donnée. Pour les systèmes linéaires à commutation, en combinant les résultats de l’estimation d’état pour les systèmes LTI et de la détection de l’instant de commutation en temps réel présentée dans le chapitre 4, nous donnons la démarche principale de l’estimation en temps réel du mode courant et l’état continu du système. Pour ce faire, on applique certains outils mathématiques : la transformation de Laplace, les outils issus du calcul opérationnel et la théorie des distributions

This PhD thesis is dedicated to the synthesis of the state estimation in a finite time by an algebraic approach (the techniques developed within the ALIEN group) for the linear time-invariant systems (LTI) subject to the external unknown disturbances, the linear time-varying systems (LTV) and the switched linear systems (SLC) in continuous time. For the LTI and LTV systems, a formal expression of state as a function of iterated integrals of the output and the input is obtained. For switched linear systems, combining the results of state estimation for LTI systems and switch instant detection presented in Chapter 4, we give the main approach of current mode estimation and the continuous state estimation in real time. To do this, one applies some mathematical tools: Laplace transforms, the operational calculus and the theory of distribution; Ce mémoire est dédié à l’étude de la synthèse de l’estimation d’état en temps fini par une approche algébrique (les techniques développées au sein de l’équipe ALIEN) pour les systèmes linéaires à paramètres invariant dans le temps (LTI) sujets à des perturbations extérieures inconnues, les systèmes linéaires à paramètres variant dans le temps (LTV) et les systèmes linéaires à commutation en temps continu (SLC). Pour les systèmes LTI et LTV, une expression formelle de l’état en fonction des intégrales itérées des sorties et de l’entrée a été donnée. Pour les systèmes linéaires à commutation, en combinant les résultats de l’estimation d’état pour les systèmes LTI et de la détection de l’instant de commutation en temps réel présentée dans le chapitre 4, nous donnons la démarche principale de l’estimation en temps réel du mode courant et l’état continu du système. Pour ce faire, on applique certains outils mathématiques : la transformation de Laplace, les outils issus du calcul opérationnel et la théorie des distributions

In this paper we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version the continuous exogenous input is considered as the disturbance, in the second the switching signal and in the third both of them are considered as disturbances. The solutions of the three disturbance decoupling problems will be based on geometric control theory for switched linear systems and will entail both mode-dependent and mode-independent static state feedback.

In this paper we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version the continuous exogenous input is considered as the disturbance, in the second the switching signal and in the third both of them are considered as disturbances. The solutions of the three disturbance decoupling problems will be based on geometric control theory for switched linear systems and will entail both mode-dependent and mode-independent static state feedback.

Dimirovski, Georgi M. (Dogus Author) Robust tracking control for switched linear systems with time-delay is investigated in this paper. Sufficient conditions for the solvability of robust tracking control problem are developed. Based on the theories of functional differential equations, the norm bound of the reference state of time-delay system is given. An average dwell time approach and piecewise Lyapunov functional method are utilized to design the switching control laws. By using linear matrix inequalities, the controller design problem can be solved efficiently. A simulation example shows the effectiveness of the proposed switching control laws.

International audience; This paper is concerned with the identification of switched linear MIMO state-space systems in a recursive way. Firstly, a structured subspace identification scheme for linear systems is presented which turns out to have many attractive features. More precisely, it does not require any singular value decomposition (SVD) but is derived using orthogonal projection techniques; it allows a computationally appealing implementation and it is closely related to input-output models identification. Secondly, it is shown that this method can be implemented on-line to track both the range space of the extended observability matrix and its dimension and thereby, the system matrices. Thirdly, by making use of an on-line switching times detection strategy, this method is applied to blindly identify switched systems and to label the obtained submodels. Simulation results on noisy data illustrate the abilities and the benefits of the proposed approach.

In this thesis we study a Gersgorin type theorem, spectral inequalities, and simultaneous stability of linear transformations in the setting of Euclidean Jordan algebras. For complex square matrices, the Levy-Desplanques theorem asserts that a strictly diagonally dominant matrix is invertible. The well-known Gersgorin theorem on the location of eigenvalues is equivalent to this. In the first part of the thesis, we extend the Levy-Desplanques theorem to an object in a Euclidean Jordan algebra when its Peirce decomposition with respect to a Jordan frame is given. As a consequence, we prove a Gersgorin type theorem for the spectral eigenvalues of an object in a Euclidean Jordan algebra. In matrix theory, the well known Cauchy's interlacing theorem states that if a row-column pair is deleted from a complex Hermitian matrix, then the eigenvalues of the resulting principal matrix interlace those of the original one. This result was generalized recently to the setting of simple Euclidean Jordan algebras. In the second part of the thesis, we present some consequences of this generalization and prove the dual form of the min-max theorem of Hirzebruch. One of the applications of the min-max theorem from matrix analysis is the problem of comparing the eigenvalues of Hermitian matrices A and B with those of A + B, proved by Weyl. Using the min-max theorem of Hirzebruch, we extend Weyl's inequality to the setting of simple Euclidean Jordan algebras and study some consequences of it. Using duality and complementarity ideas, and Z-transformations, in the third part of the thesis, we discuss ways of describing simultaneous stability of linear transformations on Hilbert spaces. As a consequence, we discuss the existence of common linear/quadratic Lyapunov functions for switched linear systems. In particular, we extend a recent result of Mason-Shorten on positive switched system with two constituent linear time-invariant systems to an arbitrary finite system.

In this paper, the problem of H∞ model reduction for switched linear discrete-time systems with polytopic uncertainties is investigated. A reduced-order switched model is constructed for a given robustly stable switched system, which has the same structural polytopic uncertainties as the original system, such that the resulting error system is robustly asymptotically stable and an H∞ error performance is guaranteed. A sufficient condition for the existence of the desired reduced-order model is derived and formulated in terms of a set of linear matrix inequalities. By solving the corresponding convex optimization problem in such existence condition, the vertex system of reduced-order model can be obtained, which also provides an H∞ gain for the error system between the original system and the reduced-order model. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Refereed/Peer-reviewed

Dimirovski, Georgi M. (Dogus Author) -- Conference full title: 47th IEEE Conference on Decision and Control : 9-10 December 2008, Cancun, Mexico We investigate the tracking control problem for switched linear time-varying delays systems with stabilizable and unstabilizable subsystems. Sufficient conditions for the solvability of the tracking control problem are developed. The tracking control problem of a switched time-varying delays system with stabilizable and unstabilizable subsystems is solvable if the stabilizable and unstabilizable subsystems satisfy certain conditions and admissible switching law among them. Average dwell time approach and piecewise Lyapunov functional methods are utilized to the stability analysis and controller design. A simulation example shows the effectiveness of the proposed method. This work was supported in part by Dogus University Fund for Science and Ministry of Education and Science of the Republic of Macedonia, and NSF of China under Grants 60874024 and 60574013.

The problem of inversion and flat output characterization for switched linear discrete-time systems is tackled through a unified framework. For this class of hybrid systems, we first derive algebraic conditions to conclude on invertibility, which extends the previous results of Sain and Massey [1] dealing with linear time-invariant systems. Then, the structure of the switched inverse system is provided. Finally, based on the connection with the inversion problem and the related notion of inverse dynamics, we derive conditions which enable to check whether a given output is flat. Due to space limitation, the proofs are not provided but can be found in [2].

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2007, Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2007, Bu çalışmada, bir altsistemler ailesinden ve bu altsistemler arasındaki geçişleri yöneten bir anahtarlama kuralından oluşan anahtarlanmış sistemler genel olarak incelenmiş; ve altsistemler ailesinin her bir üyesinin doğrusal olduğu durumda oluşan anahtarlanmış doğrusal sistemlerin kararlılığına ilişkin literatürde bulunan üç temel problem tanıtılmıştır. Bunlardan keyfi anahtarlama problemi olarak adlandırdığımız birinci problemde anahtarlama işareti ne olursa olsun sistemin kararlı olmasının koşullarını aranır. Kararlılaştırma problemi olarak adlandığımız ikinci problemde ise verilmiş bir altsistemler ailesini kararlı kılan bir anahtarlama işaretinin varlığı ve ne olduğu araştırılır. Çalışmamızda bu iki probleme ilişkin birincisinde ortak Lyapunov fonksiyonu bulunmasına ikincisinde ise altsistemlere ilişkin matrislerin bir Hurwitz konveks kombinasyonunun bulunmasına dayanan literatürde bulunan iki çözüm anlatılmıştır. Uygun anahtarlama işaretleri kümesini bulma problemi olarak adlandırdığımız üçüncü problem ise verilmiş bir altsistemler ailesini kararlı kılan özel anahtarlama işaretleri kümelerini bulma problemidir. Bu probleme ilişkin kendi geliştirdiğimiz bir yaklaşım sunulmuştur. Anahtarlanmış sistemlerin iteratif fonksiyonlar sistemlerine dönüştürülmesine dayanan bu yaklaşım ile anahtarlanmış sistemin kararlı olması için anahtarlama işaretindeki sabit aralıkların minimum uzunluğunun belli bir değerden büyük olmasına dayanan bir yeter koşul verilmiştir. Son olarak elde ettiğimiz sonuçlar iki örnek üzerinden değerlendirilmiş ve elde edilen sonuçların bu konuyla ilgili yapacağımız ileriki çalışmalar konusunda işaret ettiği yönler tartışılmıştır. Özellikle altsistemlere ilişkin matrislerin özvektörlerinin yakınlığına dayalı bir açıklama ile uygun anahtarlama kümesini bulma problemine ilişkin bir çözüm yoluna işaret edilmiştir., In this study, switched systems, which consist of a family of subsystems and a switching rule that controls the switching between the subsystems, are explained generally, and the three problems founded in literature on the stability of switched linear systems, which arise in the case that all the subsystems are linear, are introduced. Among these, the first one called the arbitrary switching problem deals with finding the conditions that results in the stability of the switched system independent of the switching signal. The second one called the stabilizing problem considers how to find a stabilizing switching signal for a given family of subsystems. In the thesis we explained the two approaches to find the solution of these problems which depends on the presence of common Lyapunov function for the former, and on finding a Hurwitz convex combination of the subsystem matrices for the latter. The third problem that we called the problem of finding the proper set of switching signals concerns with some special sets of switching signals forming a stable switched system for a given family of subsystems. We presented our own approach to solve this problem. By the approach of converting a switched system to an equivalent iterated function system, a sufficient condition is presented based on the minimum length of the intervals where the switching signal is constant. Finally, we discuss on some issues for future research that the study points out., Yüksek Lisans, M.Sc.

This thesis is divided into two separate parts. The first part is about Dynamic Programming for non-trivial optimal control problems. The second part introduces some useful tools for analysis of stability and performance of systems with time-varying delays. The two papers presented in the first part attacks optimal control problems with finite but rapidly increasing search space. In the first paper we try it reduce the complexity of the optimization by exploiting the structure of a certain problem. The result, if found, is an optimal solution. The second paper introduces a new general approach of relaxing the optimality constraint. The main contribution of the paper is an extension of the Bellman equality to a double inequality. This inequality is a sufficient condition for a suboptimal solution to be within a certain distance to the optimal solution. The main approach of solving the inequality in the paper is value iteration, which is shown to work well in many different applications. In the second part of the thesis, two analysis methods for systems with time-varying delays are presented in two papers. The first paper presents a set of simple graphical stability (and performance) criteria when the delays are bounded but otherwise unknown. All that is needed to verify stability is a Bode diagram of the closed loop system. For more exact computations, the last paper presents a toolbox for Matlab called Jitterbug. It calculates quadratic costs and power spectral densities of interconnected continuous-time and discrete-time linear systems. The main contribution of the toolbox is to make well known theory easily applicable for analysis of real-time systems.

In this paper disturbance decoupling problem for switched linear systems is formulated under a geometrical point of view. Necessary and sufficient conditions for the problem with standardizable condition to be solvable are given

International audience; This paper describes the development of a new methodology for searching a common quadratic Lyapunov function for switched linear systems based on differential evolution algorithm. This method aims to assure the stabilization of this class of systems. To illustrate the proposed methodology two examples are exploited.