Optimal Control for Discrete Event and Hybrid Systems∗

As time-driven and event-driven systems are rapidly coming together, the field of optimal control is presented with an opportunity to expand its horizons to these new “hybrid” dynamic systems. In this paper, we consider a general optimal control problem formulation for such systems and describe a modeling framework allowing us to decompose the problem into lower and higher-level components. We then show how to apply this setting to a class of switched linear systems with a simple event-driven switching process, in which case explicit solutions may often be obtained. For a different class of problems, where the complexity lies in the nondifferentiable nature of event-driven dynamics, we show that a different type of decomposition still allows us to obtain explicit solutions for a class of such problems. These two classes of problems illustrate the differences between various sources of complexity that one needs to confront in tackling optimal control problems for discrete-event and hybrid systems.