Computing exact automaton representations for a class of hybrid systems

It is known that one can not always have a finite state representation for hybrid systems and many decision properties can be undecidable. It was shown in Cury et al. (1995), however, that if one has a finite state automaton that generates an outer approximation to the hybrid system language, it may be possible to synthesize a discrete-state supervisor to control the hybrid system based on the approximating automaton using standard synthesis methods from the theory of discrete event systems (DESs). In this paper we develop conditions under which the automaton generated by a modification of the approximation algorithm from Niinomi et al. (1996) generates the exact language for the hybrid system.