From discrete event to hybrid systems*

Hybrid systems have emerged as a result of combining conventional time-driven dynamics with event-driven dynamics. This provides an opportunity for frameworks and methodologies developed for discrete event systems to enlarge their scope, driven by applications that range from manufacturing to command-control systems. The goal of this paper is to explore this transition from the point of view of discrete event system theory. Many hybrid systems may be viewed as consisting of a lower-level component that corresponds to time-driven physical processes, which a higher-level component with event-driven dynamics is called upon to coordinate by switching between different process operating modes. We concentrate on the formulation of optimization problems that arise in this "hybrid" setting, where the control variables affect both higher and lower level components. We also discuss a natural evolution of Perturbation Analysis (PA) techniques for discrete event systems into similar methodologies for a class of hybrid systems known as Stochastic Fluid Models (SFM) that find wide applicability in the control of communication networks.