The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Wassim M. Haddad - One of the best experts on this subject based on the ideXlab platform.
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dissipativity theory for nonlinear stochastic Dynamical Systems
IEEE Transactions on Automatic Control, 2017Co-Authors: Tanmay Rajpurohit, Wassim M. HaddadAbstract:In this paper, we develop stochastic dissipativity theory for nonlinear Dynamical Systems using basic input-output and state properties. Specifically, a stochastic version of dissipativity using both an input-output as well as a state dissipation inequality in expectation for controlled Markov diffusion processes is presented. The results are then used to derive extended Kalman–Yakubovich–Popov conditions for characterizing necessary and sufficient conditions for stochastic dissipativity of stochastic Dynamical Systems using two-times continuously differentiable storage functions. In addition, feedback interconnection stability in probability results for stochastic Dynamical Systems are developed thereby providing a generalization of the small gain and positivity theorems to stochastic Systems.
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nonlinear Dynamical Systems and control a lyapunov based approach
2008Co-Authors: Wassim M. Haddad, Vijaysekhar ChellaboinaAbstract:Conventions and Notation xv Preface xxi Chapter 1. Introduction 1 Chapter 2. Dynamical Systems and Differential Equations 9 Chapter 3. Stability Theory for Nonlinear Dynamical Systems 135 Chapter 4. Advanced Stability Theory 207 Chapter 5. Dissipativity Theory for Nonlinear Dynamical Systems 325 Chapter 6. Stability and Optimality of Feedback Dynamical Systems 411 Chapter 7. Input-Output Stability and Dissipativity 471 Chapter 8. Optimal Nonlinear Feedback Control 511 Chapter 9. Inverse Optimal Control and Integrator Backstepping 557 Chapter 10. Disturbance Rejection Control for Nonlinear Dynamical Systems 603 Chapter 11. Robust Control for Nonlinear Uncertain Systems 649 Chapter 12. Structured Parametric Uncertainty and Parameter-Dependent Lyapunov Functions 719 Chapter 13. Stability and Dissipativity Theory for Discrete-Time Nonlinear Dynamical Systems 763 Chapter 14. Discrete-Time Optimal Nonlinear Feedback Control 845 Bibliography 901 Index 939
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Reversibility and PoincarÉ Recurrence in Linear Dynamical Systems
IEEE Transactions on Automatic Control, 2008Co-Authors: Sergey G. Nersesov, Wassim M. HaddadAbstract:In this paper, we study the Poincare recurrence phenomenon for linear Dynamical Systems, that is, linear Systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincare recurrence and review sufficient conditions for nonlinear Dynamical Systems that ensure that the system exhibits Poincare recurrence. Furthermore, we establish necessary and sufficient conditions for Poincare recurrence in linear Dynamical Systems. In addition, we show that in the case of linear Systems the absence of volume-preservation is equivalent to the absence of Poincare recurrence implying irreversibility of a Dynamical system. Finally, we introduce the notion of output reversibility and show that in the case of linear Systems, Poincare recurrence is a sufficient condition for output reversibility.
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Control Vector Lyapunov Functions for Large-Scale Impulsive Dynamical Systems
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: Sergey G. Nersesov, Wassim M. HaddadAbstract:Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we provide generalizations to the recent extensions of vector Lyapunov theory for continuous-time Systems to address stability and control design of impulsive Dynamical Systems via vector Lyapunov functions. Specifically, we provide a generalized comparison principle involving hybrid comparison dynamics that are dependent on comparison system states as well as the nonlinear impulsive Dynamical system states. Furthermore, we develop stability results for impulsive Dynamical Systems that involve vector Lyapunov functions and hybrid comparison inequalities. Based on these results, we show that partial stability for state-dependent impulsive Dynamical Systems can be addressed via vector Lyapunov functions. Furthermore, we extend the novel notion of control vector Lyapunov functions to impulsive Dynamical Systems. Using control vector Lyapunov functions, we present a universal decentralized feedback stabilizer for a decentralized affine in the control nonlinear impulsive Dynamical system. These results are then used to develop decentralized controllers for large-scale impulsive Dynamical Systems with robustness guarantees against full modeling uncertainty.
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Reversibility and Poincare recurrence in linear Dynamical Systems
2006 American Control Conference, 2006Co-Authors: Sergey G. Nersesov, Wassim M. HaddadAbstract:In this paper, we study the Poincare recurrence phenomenon in linear Dynamical Systems, that is, Dynamical Systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincare recurrence and review sufficient conditions for nonlinear Dynamical Systems that ensure that the system exhibits Poincare recurrence. Furthermore, we establish necessary and sufficient conditions for Poincare recurrence in linear Dynamical Systems. Finally, we show that in the case of linear Systems the absence of volume-preservation is equivalent to the absence of Poincare recurrence implying irreversibility of a Dynamical system
Sergey G. Nersesov - One of the best experts on this subject based on the ideXlab platform.
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Reversibility and PoincarÉ Recurrence in Linear Dynamical Systems
IEEE Transactions on Automatic Control, 2008Co-Authors: Sergey G. Nersesov, Wassim M. HaddadAbstract:In this paper, we study the Poincare recurrence phenomenon for linear Dynamical Systems, that is, linear Systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincare recurrence and review sufficient conditions for nonlinear Dynamical Systems that ensure that the system exhibits Poincare recurrence. Furthermore, we establish necessary and sufficient conditions for Poincare recurrence in linear Dynamical Systems. In addition, we show that in the case of linear Systems the absence of volume-preservation is equivalent to the absence of Poincare recurrence implying irreversibility of a Dynamical system. Finally, we introduce the notion of output reversibility and show that in the case of linear Systems, Poincare recurrence is a sufficient condition for output reversibility.
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Design of finite-time stabilizing controllers for nonlinear Dynamical Systems
2007 46th IEEE Conference on Decision and Control, 2007Co-Authors: Sergey G. Nersesov, C. Nataraj, Jevon M. AvisAbstract:Finite-time stability involves Dynamical Systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such Systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using Holder continuous Lyapunov functions. In this paper, we extend the finite-time stability theory to revisit time-invariant Dynamical Systems and to address time-varying Systems. Specifically, we develop a Lyapunov based stability and control design framework for finite-time stability as well as finite-time tracking for time-varying nonlinear Dynamical Systems. Furthermore, we use vector Lyapunov function approach to study finite-time stabilization of sets for large-scale Dynamical Systems which is essential in formation control of multiple agents.
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Control Vector Lyapunov Functions for Large-Scale Impulsive Dynamical Systems
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: Sergey G. Nersesov, Wassim M. HaddadAbstract:Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we provide generalizations to the recent extensions of vector Lyapunov theory for continuous-time Systems to address stability and control design of impulsive Dynamical Systems via vector Lyapunov functions. Specifically, we provide a generalized comparison principle involving hybrid comparison dynamics that are dependent on comparison system states as well as the nonlinear impulsive Dynamical system states. Furthermore, we develop stability results for impulsive Dynamical Systems that involve vector Lyapunov functions and hybrid comparison inequalities. Based on these results, we show that partial stability for state-dependent impulsive Dynamical Systems can be addressed via vector Lyapunov functions. Furthermore, we extend the novel notion of control vector Lyapunov functions to impulsive Dynamical Systems. Using control vector Lyapunov functions, we present a universal decentralized feedback stabilizer for a decentralized affine in the control nonlinear impulsive Dynamical system. These results are then used to develop decentralized controllers for large-scale impulsive Dynamical Systems with robustness guarantees against full modeling uncertainty.
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Reversibility and Poincare recurrence in linear Dynamical Systems
2006 American Control Conference, 2006Co-Authors: Sergey G. Nersesov, Wassim M. HaddadAbstract:In this paper, we study the Poincare recurrence phenomenon in linear Dynamical Systems, that is, Dynamical Systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincare recurrence and review sufficient conditions for nonlinear Dynamical Systems that ensure that the system exhibits Poincare recurrence. Furthermore, we establish necessary and sufficient conditions for Poincare recurrence in linear Dynamical Systems. Finally, we show that in the case of linear Systems the absence of volume-preservation is equivalent to the absence of Poincare recurrence implying irreversibility of a Dynamical system
W.m. Haddad - One of the best experts on this subject based on the ideXlab platform.
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An invariance principle for nonlinear hybrid and impulsive Dynamical Systems
Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000Co-Authors: Vijaysekhar Chellaboina, S.p. Bhat, W.m. HaddadAbstract:In this paper we develop an invariance principle for Dynamical Systems possessing left-continuous flows. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive Dynamical Systems; namely, state-dependent impulsive Dynamical Systems. These results provide less conservative stability conditions for impulsive Systems as compared to classical results in literature and allow us to address the stability of limit cycles and periodic orbits of impulsive Systems.
Vijaysekhar Chellaboina - One of the best experts on this subject based on the ideXlab platform.
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nonlinear Dynamical Systems and control a lyapunov based approach
2008Co-Authors: Wassim M. Haddad, Vijaysekhar ChellaboinaAbstract:Conventions and Notation xv Preface xxi Chapter 1. Introduction 1 Chapter 2. Dynamical Systems and Differential Equations 9 Chapter 3. Stability Theory for Nonlinear Dynamical Systems 135 Chapter 4. Advanced Stability Theory 207 Chapter 5. Dissipativity Theory for Nonlinear Dynamical Systems 325 Chapter 6. Stability and Optimality of Feedback Dynamical Systems 411 Chapter 7. Input-Output Stability and Dissipativity 471 Chapter 8. Optimal Nonlinear Feedback Control 511 Chapter 9. Inverse Optimal Control and Integrator Backstepping 557 Chapter 10. Disturbance Rejection Control for Nonlinear Dynamical Systems 603 Chapter 11. Robust Control for Nonlinear Uncertain Systems 649 Chapter 12. Structured Parametric Uncertainty and Parameter-Dependent Lyapunov Functions 719 Chapter 13. Stability and Dissipativity Theory for Discrete-Time Nonlinear Dynamical Systems 763 Chapter 14. Discrete-Time Optimal Nonlinear Feedback Control 845 Bibliography 901 Index 939
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An invariance principle for nonlinear hybrid and impulsive Dynamical Systems
Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000Co-Authors: Vijaysekhar Chellaboina, S.p. Bhat, W.m. HaddadAbstract:In this paper we develop an invariance principle for Dynamical Systems possessing left-continuous flows. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive Dynamical Systems; namely, state-dependent impulsive Dynamical Systems. These results provide less conservative stability conditions for impulsive Systems as compared to classical results in literature and allow us to address the stability of limit cycles and periodic orbits of impulsive Systems.
M. Richard - One of the best experts on this subject based on the ideXlab platform.
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Signal separation for nonlinear Dynamical Systems
[Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics Speech and Signal Processing, 1992Co-Authors: C. Myers, M. RichardAbstract:The problem of signal separation for nonlinear Dynamical Systems, particularly chaotic Systems, is considered. These Systems are characterized by a stretching and folding within state space and by the presence of an attractor. Signal separation involves the separation of a received signal into two components, one of which is modeled as the output of a nonlinear Dynamical system. The authors review previous approaches to this problem and present results from the application of Kalman filtering to the signal separation problem. A Cramer-Rao bound on the performance of a signal separation algorithm in white noise is presented. The special properties of nonlinear Dynamical Systems allow state estimation that improves exponentially with the number of observations but requires special processing techniques to achieve.
