Supervisory Control of Hybrid Systems Using Approximating Hybrid Automata

Special Issue on " Control in Hybrid Systems " Abstract This paper describes an approach to synthesizing discrete controllers for hybrid systems based on finite-state approximations of the hybrid system dynamics. The plant is a hybrid system with continuous dynamics that can be switched by a discrete-valued input signal. The information available to the supervisory controller is an event signal that indicates when the continuous state trajectory encounters hypersurfaces in the continuous state space, corresponding to limits or thresholds detected by sensors in the system. The control problem is to synthesize a supervisor that selects the plant input signal based on the observed events to assure the closed-loop system satisfies the design specifications. Previous results on approximating the hybrid system dynamics with finite-state transition systems are reviewed, and a new procedure is presented to identify how an approximation should be refined if it is too coarse to solve the control synthesis problem. The paper emphasizes the theory for supervisory control synthesis for a general class of hybrid systems. The concluding section discusses the practical implications of the theoretical results and prospects for developing tools for computer-aided design of hybrid system controllers.