Hybrid Automata with Finite Bisimulatioins

The analysis, veri cation, and control of hybrid automata with nite bisimulations can be reduced to nite-state problems. We advocate a time-abstract, phasebased methodology for checking if a given hybrid automaton has a nite bisimulation. First, we factor the automaton into two components, a boolean automaton with a discrete dynamics on the nite state space B and a euclidean automaton with a continuous dynamics on the in nite state space R. Second, we investigate the phase portrait of the euclidean component. In this fashion, we obtain new decidability results for hybrid systems as well as new, uniform proofs of known decidability results. For example, we prove that if two hybrid automata have nite bisimulations, and both can be calibrated to a common time scale, then their product also has a nite bisimulation.