Local Mean Payoff Supervisory Control under Partial Observation

The problem under investigation in this work is local mean payoff supervisory control of partially observed discrete event systems. The system is modeled as a weighted finite state automaton and weight flows are generated with transitions. The local mean payoff over a finite number of events may serve as a measure of stability or robustness of the weight flows. The range of events to evaluate the local mean payoff is termed a window, which slides along transitions. The window is called fuzzy due to the presence of unobservable events. A supervisor is designed to ensure that the mean payoff within each fuzzy window always lies in certain interval. In addition, qualitative properties like safety and liveness are also required. Then the partial observation supervisory control problem is transformed to a two-player safety game on the properly defined windowed bipartite transition system. By analyzing the game, we propose a method to synthesize supervisors that provably solve the original supervisory control problem.