Showing papers by "Claude Samson published in 1999"

Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics

Abstract: Exponential stabilization of nonlinear driftless ane control systems is addressed with the concern of achieving robustness with respect to imperfect knowledge of the system's control vector elds. In order to satisfy this robustness requirement, and inspired by Bennani and Rouchon (1) where the same issue was rst addressed, we consider a control strategy which consists in applying periodically updated open-loop controls that are continuous with respect to state initial conditions. These controllers are more precisely described as continuous time-periodic feedbacks associated with a specic dynamic extension of the original system. Sucient conditions which, if they are satised by the control law, ensure that the control is a robust exponential stabilizer for the extended system are given. Explicit and simple control expressions which satisfy these conditions in the case of n- dimensional chained systems are proposed. A constructive algorithm for the design of such control laws, which applies to any (suciently regular) driftless control system, is described.

Non-robustness of continuous homogeneous stabilizers for affine control systems

Abstract: A simple definition of robustness of asymptotic stabilizers with respect to modeling errors is adopted. Two theorems giving sufficient conditions for the non-robustness of continuous homogeneous /spl rho/-exponential stabilizers are then stated; the first one applies to systems that may contain a drift term, while the second one concerns driftless systems. One of the consequences of these results is that for chained form systems, no continuous homogeneous /spl rho/-exponential stabilizer (several of which exist in the literature) can be robust in the sense defined herein. Two examples illustrate applications of these results.

A note on the design of homogeneous time-varying stabilizing control laws for driftless controllable systems via oscillatory approximation of Lie brackets in closed-loop

Abstract: A constructive method for time-varying stabilization of smooth driftless controllable systems is developed. It provides time-varying homogeneous feedback laws that are continuous and smooth away from the origin. These feedbacks make the closed-loop system globally exponentially asymptotically stable if the control system is homogeneous with respect to a family of dilations, and, using local homogeneous approximation of control systems, locally exponentially asymptotically stable otherwise. The method uses some known algorithms that construct oscillatory control inputs to approximate motion in the direction of iterated Lie brackets, that we adapt to the closed-loop context.

On the robust stabilization of chained systems by continuous feedback

Abstract: We address the problem of robust feedback stabilization of nonlinear chained systems. Some Lipschitz-continuous time-varying feedback are proposed. They make the origin of the nominal system locally and asymptotically stable. For unmodelled dynamics with small enough magnitude, in dimension 3 or 4, these control laws also stabilize the perturbed systems, while a restriction on (the "direction" of) the perturbation is required for higher dimensions.

Robust point-stabilization of nonlinear affine control systems

Abstract: Exponential stabilization of nonlinear driftless affine control systems is addressed with the concern of achieving robustness with respect to imperfect knowledge of the system’s control vector fields. The present paper gives an overview of the results developed by the authors in [11], and provides new results on the robustness with respect to sampling of the control laws. Control design for a dynamic extension of the original system is also considered. This study is inspired by [1], where the same robustness issue was first addressed. It is further motivated by the fact, proven in [7], according to which no continuous homogeneous time-periodic state-feedback can be a robust exponential stabilizer in the sense considered here. Hybrid open-loop/feedback controllers, more precisely described as continuous time-periodic feedbacks associated with a specific dynamic extension of the original system, are considered instead

Simultaneous image classification and restoration using a variational approach

Abstract: Herein, we present a variational model devoted to image classification coupled with an edge-preserving regularization process. In the last decade, the variational approach has proven its efficiency in the field of edge-preserving restoration. In this paper, we add a classification capability which contributes to provide images compound of homogeneous regions with regularized boundaries. The soundness of this model is based on the works developed on the phase transition theory in mechanics. The proposed algorithm is fast, easy to implement and efficient. We compare our results on both synthetic and satellite images with the ones obtained by a stochastic model using a Potts regularization.