Synthesis of supervisory controllers for hybrid systems based on approximating automata

Considers a class of continuous-time hybrid systems with discrete-valued input signals and event-based output signals. The internal continuous-state dynamics depend on the value of the input signal, and output events occur when the state trajectory encounters threshold manifolds in the state space. The supervisor is allowed to switch the input signal value when threshold events are observed. The objective is to synthesize a nonblocking supervisor (in the ω-language sense) such that the threshold event language is within given upper and lower bounds. The authors show how the problem can be converted into a supervisor synthesis for a discrete event system. A solution can then be obtained through the construction of a finite-state generator with a language which is an outer approximation to the exact original DES plant for the original hybrid system. An iterative algorithm is presented for constructing increasingly refined outer approximations. It is shown that supervisors synthesized for the approximating automata achieve the control specifications when applied to the original hybrid system