Control Using Logic-Based Switching.

Between the well-studied areas of discontinuous control on the one hand and sampled data control 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. More often than not the predominately logical component within such a system is called a supervisor, a mode changer, 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. 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. The paper gives 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. Three of the logics, called prerouted switching, hysteresis switching and dwell-time switching respectively, are simple strategies capable of determining in real time which candidate controller should be put in feedback with a process in order to achieve desired closed-loop performance. The fourth, called cyclic switching, has been devised to solve the long-standing stabilizability problem which arises in the synthesis of identifier-based adaptive controllers because of the existence of points in parameter space where the estimated model upon which certainty equivalence synthesis is based, loses stabilizability.