Applying Jump Systems Control Theory to Discrete Event-Driven Hybrid Systems

For over twenty years, hybrid systems, involving both a discrete-valued state component and a continuous-valued state component (evolving in either discrete or continuous time), have challenged control engineers interested in expanding the applications of control theory. In particular, the hybrid system representation has motivated the formulation of "fault-tolerant" optimal control problems for systems subject to abrupt changes in their structure, parameters or operating environment. One approach has been the development of optimal controllers for jump linear systems. Strong theoretical results are currently limited, however, to Markov and semi-Markov jump processes, when change in the system structure are perfectly observed. During the same two decades, theory and methods for the analysis of discrete event systems have been developed. Recently the control of discrete event systems has received significant attention. This paper is directed toward the application of jump systems control theory to the control of continuous variable processes driven by discrete event systems.