Results 1  10
of
47
Further constructions of strict Lyapunov functions for timevarying systems
 in Proceedings of the American Control Conference
, 2005
"... We provide explicit closed form expressions for strict Lyapunov functions for timevarying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters. This provides a discrete tim ..."
Abstract

Cited by 28 (5 self)
 Add to MetaCart
(Show Context)
We provide explicit closed form expressions for strict Lyapunov functions for timevarying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters. This provides a discrete time analog of our previous continuous time Lyapunov function constructions. We also construct explicit strict Lyapunov functions for systems satisfying nonstrict discrete time analogs of the conditions from Matrosov’s Theorem. We use our methods to build strict Lyapunov functions for timevarying hybrid systems that contain mixtures of continuous and discrete time evolutions. Key Words: Strict Lyapunov functions, discrete and hybrid timevarying systems. 1
Results on inputtostate stability for hybrid systems
, 2005
"... We show that, like continuoustime systems, zeroinput locally asymptotically stable hybrid systems are locally inputtostatestable (LISS). We demonstrate by examples that, unlike continuoustime systems, zeroinput locally exponentially stable hybrid systems may not be LISS with linear gain, inpu ..."
Abstract

Cited by 27 (2 self)
 Add to MetaCart
We show that, like continuoustime systems, zeroinput locally asymptotically stable hybrid systems are locally inputtostatestable (LISS). We demonstrate by examples that, unlike continuoustime systems, zeroinput locally exponentially stable hybrid systems may not be LISS with linear gain, inputtostate stable (ISS) hybrid systems may not admit any ISS Lyapunov function, and nonuniform ISS hybrid systems may not be (uniformly) ISS. We then provide a strengthened ISS condition as an equivalence to the existence of an ISS Lyapunov function for hybrid systems. This strengthened condition reduces to standard ISS for continuoustime and discretetime systems. Finally under some other assumptions we establish the equivalence among ISS, several asymptotic characterizations of ISS, and the existence of an ISS Lyapunov function for hybrid systems.
Stability analysis of hybrid systems via smallgain theorems,” 2006
"... Abstract. We present a general approach to analyzing stability of hybrid systems, based on inputtostate stability (ISS) and smallgain theorems. We demonstrate that the ISS smallgain analysis framework is very naturally applicable in the context of hybrid systems. Novel Lyapunovbased and LaSal ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We present a general approach to analyzing stability of hybrid systems, based on inputtostate stability (ISS) and smallgain theorems. We demonstrate that the ISS smallgain analysis framework is very naturally applicable in the context of hybrid systems. Novel Lyapunovbased and LaSallebased smallgain theorems for hybrid systems are presented. An illustrative application of the proposed approach in the context of a quantized feedback control problem is treated in detail. The reader does not need to be familiar with ISS or smallgain theorems to be able to follow the paper. 1
Quasioptimal robust stabilization of control systems
, 2005
"... Abstract. In this paper, we investigate the problem of semiglobal minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is shown that, in the absence of minimal time singular trajectories, the solutions of the clos ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
Abstract. In this paper, we investigate the problem of semiglobal minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is shown that, in the absence of minimal time singular trajectories, the solutions of the closedloop system converge to the origin in quasi minimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise, external disturbances and actuator noise. Key words. Hybrid feedback, robust stabilization, measurement errors, actuator noise, external disturbances, optimal control, singular trajectory, subRiemannian geometry. AMS subject classifications. 93B52, 93D15
On hybrid controllers that induce inputtostate stability with respect to measurement noise
, 2005
"... For a class of nonlinear systems affine in controls and with unknown high frequency gain, we develop a hybrid control strategy that guarantees (practical) global inputtostate stability (ISS) with respect to measurement noise. We provide a design procedure for the hybrid controller and apply it t ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
For a class of nonlinear systems affine in controls and with unknown high frequency gain, we develop a hybrid control strategy that guarantees (practical) global inputtostate stability (ISS) with respect to measurement noise. We provide a design procedure for the hybrid controller and apply it to Freeman’s counterexample and minimumphase relative degree one systems.
Unicycle coverage control via hybrid modeling
 IEEE Transactions on Automatic Control
, 2010
"... This paper presents gradientdescent coverage algorithms for a group of nonholonomic vehicles. Similarly to previous approaches, the deployment strategy relies on Locational Optimization techniques and algorithms are distributed in the sense of the Delaunay graph. In order to deal with unicycle dyna ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
This paper presents gradientdescent coverage algorithms for a group of nonholonomic vehicles. Similarly to previous approaches, the deployment strategy relies on Locational Optimization techniques and algorithms are distributed in the sense of the Delaunay graph. In order to deal with unicycle dynamics and guarantee performance, we introduce several vehicle modes and integrate them in a hybrid system We then analyze the algorithms with a recently introduced invariance principle for hybrid systems. I.
Semiglobal minimal time hybrid robust stabilization of analytic driftless controlaffine systems
, 2005
"... We investigate the problem of semiglobal minimal time robust stabilization of analytic driftless controlaffine systems, by means of a hybrid state feedback law. Our main result is that, in the absence of singular minimal time solutions, the solutions of the closedloop system converge to the orig ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
We investigate the problem of semiglobal minimal time robust stabilization of analytic driftless controlaffine systems, by means of a hybrid state feedback law. Our main result is that, in the absence of singular minimal time solutions, the solutions of the closedloop system converge to the origin in quasiminimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise and external disturbances.
A Realtime Framework for Model Predictive Control of ContinuousTime Nonlinear Systems
, 2005
"... A new formulation of continuoustime nonlinear model predictive control (NMPC) is developed which accounts for dynamics associated with minimization of the optimal control problem. In doing so, it is shown that the stability of NMPC can be maintained for fast processes in which the computation time ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
A new formulation of continuoustime nonlinear model predictive control (NMPC) is developed which accounts for dynamics associated with minimization of the optimal control problem. In doing so, it is shown that the stability of NMPC can be maintained for fast processes in which the computation time is significant with respect to the process dynamics. Our framework generalizes recent results for piecewise constant NMPC of continuoustime processes.
On two hybrid robust optimal stabilization problems
 in "Proceedings of the 13th IFAC Workshop on Control Applications of optimisation (CAO’06)", Internat
"... Abstract: We report on some recent results obtained by the authors concerning robust hybrid stabilization of control systems. In (Prieur and Trélat, 2005a), we state a result of semiglobal minimal time robust stabilization for analytic control systems with controls entering linearly, by means of a ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract: We report on some recent results obtained by the authors concerning robust hybrid stabilization of control systems. In (Prieur and Trélat, 2005a), we state a result of semiglobal minimal time robust stabilization for analytic control systems with controls entering linearly, by means of a hybrid state feedback law, under the main assumption of the absence of minimal time singular trajectories. In (Prieur and Trélat, 2005c), we investigate the Martinet case, which is a model case in IR3 where singular minimizers appear, and show that such a stabilization result still holds. Namely, in both cases, we prove that the solutions of the closedloop system converge to the origin in quasi minimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise, external disturbances and actuator errors.Copyright c © 2006 IFAC