17 research outputs found
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
Control Lyapunov Functions and Stabilization by Means of Continuous Time-Varying Feedback
For a general time-varying system, we prove that existence of an "Output
Robust Control Lyapunov Function" implies existence of continuous time-varying
feedback stabilizer, which guarantees output asymptotic stability with respect
to the resulting closed-loop system. The main results of the present work
constitute generalizations of a well-known result towards feedback
stabilization due to J. M. Coron and L. Rosier concerning stabilization of
autonomous systems by means of time-varying periodic feedback.Comment: Submitted for possible publication to ESAIM Control, Optimisation and
Calculus of Variation
Lyapunov stabilizability of controlled diffusions via a superoptimality principle for viscosity solutions
We prove optimality principles for semicontinuous bounded viscosity solutions
of Hamilton-Jacobi-Bellman equations. In particular we provide a representation
formula for viscosity supersolutions as value functions of suitable obstacle
control problems. This result is applied to extend the Lyapunov direct method
for stability to controlled Ito stochastic differential equations. We define
the appropriate concept of Lyapunov function to study the stochastic open loop
stabilizability in probability and the local and global asymptotic
stabilizability (or asymptotic controllability). Finally we illustrate the
theory with some examples.Comment: 22 page
Singularities of viscosity solutions and the stabilization problem in the plane
International audienceWe study the general problem of globally asymp- totically controllable affine systems in the plane. As preliminaries we present some results of independent interest. We study the regularity of some sets related to semiconcave viscosity supersolutions of Hamilton-Jacobi-Bellman equations. Then we deduce a construction of stabilizing feedbacks in the plane