Compensation of infinite-dimensional input dynamics

Abstract

Abstract We present a tutorial introduction to methods for stabilization of systems with infinite-dimensional input dynamics including delays, diffusion, counter-convection and wave propagation. The methods are based on techniques originally developed for boundary control of partial differential equations. We consider multi-input linear time-invariant systems with input dynamics governed by distributed delays, and diffusion with counter-convection or wave PDEs. For the special case of single-input linear time-invariant systems with a single discrete delay we prove robustness of the control law to a small uncertainty in the delay and in the case of completely unknown delay we present an adaptive control approach. For this special case, we also present a method for compensating arbitrarily large but known time-varying delays. Finally, we consider nonlinear control problems in the presence of arbitrarily long input delays.