Optimal Control of a Class of Hybrid Systems

Abstract—We present a modeling framework for hybrid systems intended to capture the interaction of event-driven and time-driven dynamics. This is motivated by the structure of many manufac-turing environments where discrete entities (termed jobs) are pro-cessed through a network of workcenters so as to change their physical characteristics. Associated with each job is a temporal state subject to event-driven dynamics and a physical state subject to time-driven dynamics. Based on this framework, we formulate and ana-lyze a class of optimal control problems for single-stage processes. First-order optimality conditions are derived and several proper-ties of optimal state trajectories (sample paths) are identified which significantly simplify the task of obtaining explicit optimal control policies. Index Terms—Hybrid system, nonsmooth optimization, optimal control. I