Supervisory control problems of hierarchical finite state machines

The situation under consideration is that of a given Discrete Event System (DES), whose behavior has to be modified by means of a feedback control (named Supervisor) in order to achieve a given set of requirements that the initial DES did not satisfy. To do so, the DES is modeled as a Hierarchical Finite State Machine (HFSM). Further, instead of translating the HFSM to ordinary state machines and using classical synthesis tools on the resulting FSM, we here present algorithms that solve the Supervisory Control Problem (for a particular case of forbidden state avoidance problem) as well as the Optimal Control Problem without expanding the HFSM.