Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization

The paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robusteness of patchy feedback controls in the presence of measurement errors and external disturbances.Comment: 22 page

Quasi-optimal robust stabilization of control systems

In this paper, we investigate the problem of semi-global 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 closed-loop 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

Nearly Optimal Patchy Feedbacks for Minimization Problems with Free Terminal Time

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 pre-assigned accuracy.Comment: 13 pages, 3 figures. in v2: Fixed few misprint

On feedback strategies in control problems and differential games

This thesis consists of two parts. In the first part we study the existence and uniqueness of Nash equilibrium solutions for a class of infinite horizon, non-cooperative differential games. The second part is concerned with the construction of nearly-optimal patchy feedbacks, for problems of optimal control

On the construction of nearly time optimal continuous feedback laws around switching manifolds

In this paper, we address the question of the construction of a nearly time optimal feedback law for a minimum time optimal control problem, which is robust with respect to internal and external perturbations. For this purpose we take as starting point an optimal synthesis, which is a suitable collection of optimal trajectories. The construction we exhibit depends exclusively on the initial data obtained from the optimal feedback which is assumed to be known