Control Using Logic-Based Switching

Between the well-studied areas of discontinuous control [1], [2] on the one hand and sampled data control [3] on the other lies the largely unexplored area of 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 {e.g., [4]}. More often than not the predominately logical component within such a system is called a supervisor [5], a mode changer [6], a gain scheduler, or something similar. Within the last decade a number of analytical studies of such systems have emerged, mainly in the area of self-adjusting control [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. These studies and others have shown that much can be gained by using logic-based switching together with more familiar techniques in the synthesis of feedback controls. The overall models of systems composed of such logics together with the processes they are intended to control are concrete examples of hybrid dynamical systems [17, 18, 19]. The aim of this paper is to give a brief tutorial review of four different classes of hybrid systems of this type — each consists of a continuous-time process to be controlled, a parameterized family of candidate controllers, and an event driven switching logic.