Lectures on Control Using Logic and Switching

The overall objective of these lectures is to overview a variety of methods for synthesizing and analyzing logic-based switching control systems. By a logic-based switching controller is meant a controller whose subsystems include not only familiar dynamical components {integrators, summers, gains, etc.} but logic-driven elements as well. The overall models of systems composed of such logics together with the processes they are intended to control, are concrete examples of what might be called “hybrid dynamical systems.” An important category of such systems are those consisting of a process to be controlled, a family of fixed-gain or variable-gain candidate controllers, and an “event-driven switching logic” called a supervisor whose job is to determine in real time which controller should be applied to the process. Examples of supervisory control systems include re-configurable systems, fault correction systems, and certain types of parameter-adaptive systems. Major reasons for introducing logic and switching are to deal with communication, actuator and sensor constraints, with model uncertainty, with unforeseen events or to avoid performing difficult tasks e.g., precise equipment calibration which might otherwise be necessary were one to consider only conventional controls. The aim of these lectures in is to provide an overview of algorithms with these capabilities, as well as to discuss various techniques for analyzing the types of switched systems which result.