Predictor feedback: Time-varying, adaptive, and nonlinear

Abstract

We present a tutorial introduction to methods for stabilization of systems with long input delays-the so-called "predictor feedback" techniques. The methods are based on techniques originally developed for boundary control of partial differential equations using the "backstepping" approach. We start with a consideration of linear systems, first with a known delay and then subject to a small uncertainty in the delay. Then we study linear systems with constant delays that are completely unknown, which requires an adaptive control approach. For linear systems, we also present a method for compensating arbitrarily large but known time-varying delays. Next, we consider nonlinear control problems in the presence of arbitrarily long input delays. Finally, we close with a design for general nonlinear systems with delays that have a general dependency on the system state. © 2012 Springer-Verlag GmbH Berlin Heidelberg.