OPTIMAIL CONTROL OF A CLASS OF HYBRID SYSTEMS

We develop a modelinl: framework for a class of hybrid systems which arise in many manufacturing environments and study the optimal control of such models. The framework uses a queueing network to describe the movement of jobs through a manufacturing facility. As jobs wait in queues arid get processed in servers, their physical Characteristics: change according to differential equations. The state of each job has a temporal component whose evolution is described by discrete-event queueing dynamics, and a physical component whose evolution is described hy time-driven dynamics. Calculus of variations techniques are used to derive optimal policies. 1. IbITRODUCTION Hybrid systems are those that combine event-driven dynamics with time-driven dynamics. Several modeling frameworks have been proposed to study such systems. These frameworks can be broadly divided into two categories: Those that extend the traditional event-driven models to include time-driven dynamics; and those that extend the traditional time-driven models to include eventdriven dynamics. Examples from the fist category include extensions to the timed state automata and Petri net models