Results 1  10
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19
Global Asymptotic Controllability Implies Input to State Stabilization
, 2003
"... We study nonlinear systems with observation errors. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state stable with respect to actuator errors. Extensions for full ..."
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Cited by 10 (8 self)
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We study nonlinear systems with observation errors. The main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable (GAC) control affine systems that render the closed loop systems input to state stable with respect to actuator errors. Extensions for fully nonlinear GAC systems with actuator errors are also discussed.
Semiconcavity results for optimal control problems admitting no singular minimizing controls
 Ann. Inst. H. Poincaré Non Linéaire
"... Abstract. Semiconcavity results have generally been obtained for optimal control problems in absence of state constraints. In this paper, we prove the semiconcavity of the value function of an optimal control problem with endpoint constraints for which all minimizing controls are supposed to be non ..."
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Cited by 6 (2 self)
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Abstract. Semiconcavity results have generally been obtained for optimal control problems in absence of state constraints. In this paper, we prove the semiconcavity of the value function of an optimal control problem with endpoint constraints for which all minimizing controls are supposed to be nonsingular. hal00862030, version 1 15 Sep 2013 1.
Asymptotic controllability and inputtostate stabilization: the effect of actuator errors, Optimal control, stabilization and nonsmooth analysis
 Lecture Notes in Control and Information Sciences, V. 301
, 2004
"... ..."
Lyapunov functions and feedback in nonlinear control
 Optimal Control, Stabilization and Nonsmooth Analysis, volume 301 of Lecture
"... Summary. The method of Lyapunov functions plays a central role in the study of the controllability and stabilizability of control systems. For nonlinear systems, it turns out to be essential to consider nonsmooth Lyapunov functions, even if the underlying control dynamics are themselves smooth. We s ..."
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Cited by 6 (1 self)
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Summary. The method of Lyapunov functions plays a central role in the study of the controllability and stabilizability of control systems. For nonlinear systems, it turns out to be essential to consider nonsmooth Lyapunov functions, even if the underlying control dynamics are themselves smooth. We synthesize in this article a number of recent developments bearing upon the regularity properties of Lyapunov functions. A novel feature of our approach is that the guidability and stability issues are decoupled. For each of these issues, we identify various regularity classes of Lyapunov functions and the system properties to which they correspond. We show how such regularity properties are relevant to the construction of stabilizing feedbacks. Such feedbacks, which must be discontinuous in general, are implemented in the sampleandhold sense. We discuss the equivalence between openloop controllability, feedback stabilizability, and the existence of Lyapunov functions with appropriate regularity properties. The extent of the equivalence confirms the cogency of the new approach summarized here. 1
Closed Loop Stabilization of Planar Bilinear Switched Systems
"... In this paper we address the closed loop switched stabilization problem for planar bilinear systems under the assumption that the control is one dimensional and takes only the values 0 and 1. We construct a class of statestaticmemoryless stabilizing feedback laws which preserve the properties of o ..."
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Cited by 5 (2 self)
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In this paper we address the closed loop switched stabilization problem for planar bilinear systems under the assumption that the control is one dimensional and takes only the values 0 and 1. We construct a class of statestaticmemoryless stabilizing feedback laws which preserve the properties of open loop switching signals. In order to prove the stability of the implemented system, we use Lyapunov techniques for differential equations with discontinuous righthand side. Finally we point out some possible extensions of our result and compare it with related results previously proven by other authors.
Nearly time optimal stabilizing patchy feedbacks, Preprint Arxiv
, 2005
"... Abstract. We consider the time optimal stabilization problem for a nonlinear control system ˙x = f(x, u). Let τ(y) be the minimum time needed to steer the system from the state y ∈ R n to the origin, and call A(T) the set of initial states that can be steered to the origin in time τ(y) ≤ T. Given a ..."
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Cited by 4 (1 self)
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Abstract. We consider the time optimal stabilization problem for a nonlinear control system ˙x = f(x, u). Let τ(y) be the minimum time needed to steer the system from the state y ∈ R n to the origin, and call A(T) the set of initial states that can be steered to the origin in time τ(y) ≤ T. Given any ε> 0, in this paper we construct a patchy feedback u = U(x) such that every solution of ˙x = f(x, U(x)), x(0) = y ∈ A(T) reaches an εneighborhood of the origin within time τ(y) + ε.
Nonpathological Lyapunov functions and discontinuous Carathéodory systems
, 2004
"... Differential equations with discontinuous righthand side and solutions intended in Carathéodory sense are considered. For these equations sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle ..."
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Cited by 1 (0 self)
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Differential equations with discontinuous righthand side and solutions intended in Carathéodory sense are considered. For these equations sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle is also proven.
ROBUST STABILIZATION OF NONLINEAR CONTROL SYSTEMS BY MEANS OF HYBRID FEEDBACKS
"... Abstract. The general problem under study in this paper is the robust asymptotic stabilization of nonlinear systems. Different types of systems are considered: the Artstein’s circles, the systems which are asymptotically controllable to the origin and also the chained systems. We recall some results ..."
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Cited by 1 (0 self)
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Abstract. The general problem under study in this paper is the robust asymptotic stabilization of nonlinear systems. Different types of systems are considered: the Artstein’s circles, the systems which are asymptotically controllable to the origin and also the chained systems. We recall some results on the stabilization by means of hybrid feedback laws (namely controller with a mixed continuous/discrete component) and by means of discontinuous feedbacks. We note that hybrid feedbacks yield a robust stabilization property with respect to measurement noise, actuator errors and exogeneous disturbances, for a larger class of solutions than those obtained with discontinuous statefeedbacks. 1.
Nearly Optimal Patchy Feedbacks for Minimization Problems with Free Terminal Time
, 708
"... Abstract. The paper is concerned with a general optimization problem for a nonlinear control system, in the presence of a running cost and a terminal cost, with free terminal time. We prove the existence of a patchy feedback whose trajectories are all nearly optimal solutions, with preassigned accu ..."
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Abstract. The paper is concerned with a general optimization problem for a nonlinear control system, in the presence of a running cost and a terminal cost, with free terminal time. We prove the existence of a patchy feedback whose trajectories are all nearly optimal solutions, with preassigned accuracy. Consider a general optimization problem min T,u(·)