COORDINATED FEEDBACK AND SWITCHING FOR WAVE SUPPRESSION

摘要

This work focuses on the problem of coordinating feedback and switching for the stabilization of the zero solution of the one-dimensional Kuramoto-Sivashinsky equation (KSE) with periodic boundary conditions and input constraints. Galerkin's method is initially used to derive a finite-dimensional system that captures the dominant dynamics of the KSE for a given value of the instability parameter. This ODE system is then used as the basis for the integrated synthesis, via Lyapunov techniques, of stabilizing nonlinear feedback controllers together with switching laws that orchestrate the switching between the admissible control actuator configurations, in a way that respects input constraints, accommodates inherently conflicting control objectives, and guarantees closed-loop stability. The theoretical results are successfully illustrated through computer simulations of the closed-loop system using a high-order discretization of the KSE.