SYNTHESIS OF SUPERVISORY CONTROLLERS FOR HYBRID SYSTEMS BASED ON APPROXIMATING AUTOMATA

This paper concerns the synthesis of supervisory controllers for a cla ss of continuous-time hybrid systems with discrete-valued input signal s that select differential inclusions for continuous-valued state traj ectories and event-valued output signals generated by threshold crossi ngs in the continuous state space. The supervisor is allowed to switch thr input signal value when threshold events are observed, The object ive is to synthesize a nonblocking supervisor such that the set of pos sible sequences of control and threshold event pairs for the closed-lo op system lies between given upper and lower bounds in the sense of se t containment. We show how this problem can be converted into a superv isor synthesis problem for a standard controlled discrete-event system (DES), A finite representation may not exist for the exact DES model of the hybrid system, however. To circumvent this difficulty, we prese nt an algorithm Tor constructing finite-state Muller automata that acc ept outer approximations to the exact controlled threshold-event langu age, and we demonstrate that supervisors that solve the synthesis prob lem for the approximating automata achieve the control specifications when applied to the original hybrid system.