Switching and Logic in Adaptive Control

Prof. Joao Hespanha, Department of Electrical Engineering, University of Southern California

In this talk, we review recent results on the use of switching and logic in the context of adaptive control. The basic problem around which this talk is centered is the control of poorly modeled systems. Our paradigm of choice to undertake this problem consists of an architecture in which a high-level, logic-based supervisor orchestrates the switching between a family of candidate controllers so as to achieve some desired behavior for the closed-loop system. The need for switching arises from the fact that no single candidate controller would be capable, by itself, of guaranteeing good performance when connected with the poorly modeled process.

We start by considering a simple problem in noise suppression to motivate the overall control architecture, and proceed to show how it generalizes to large classes of regulation problems that arise in adaptive control. We shall see that these problems can be reduced to that of supervising a switched dynamical system using a suitably defined logic. The resulting closed-loop system is hybrid in that it combines differential equations with discrete logic. In this talk, we also review some of the tools that can be used to analyze this type of systems in the context of adaptive control.