A computational procedure for bisimulation of hybrid dynamical systems

The problem of finding a finite state symbolic model which is bisimilar to a hybrid dynamical system (HDS) and has the minimum number of states is considered. The solution to this problem may fail to exist and the conditions for existence of solution are not completely known. In this paper, we propose a computational procedure for this problem. The procedure is based on computing the behaviors up to a finite length for a finite set of samples from the state space. No time discretization is applied. No stability assumptions have been made. The requirements for the success of the proposed procedure are the existence of a bisimulation and taking an enough number of samples from the state space. Although this number is not known currently, the result is still useful due to the difficult nature of the problem. It is possible to increase the confidence in correctness of the solution by iterating the procedure. The results are applied to an example HDS.