40,224 research outputs found
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
Time-varying Projected Dynamical Systems with Applications to Feedback Optimization of Power Systems
This paper is concerned with the study of continuous-time, non-smooth
dynamical systems which arise in the context of time-varying non-convex
optimization problems, as for example the feedback-based optimization of power
systems. We generalize the notion of projected dynamical systems to
time-varying, possibly non-regular, domains and derive conditions for the
existence of so-called Krasovskii solutions. The key insight is that for
trajectories to exist, informally, the time-varying domain can only contract at
a bounded rate whereas it may expand discontinuously. This condition is met, in
particular, by feasible sets delimited via piecewise differentiable functions
under appropriate constraint qualifications. To illustrate the necessity and
usefulness of such a general framework, we consider a simple yet insightful
power system example, and we discuss the implications of the proposed
conditions for the design of feedback optimization schemes
- …