Local Mean Payoff Supervisory Control for Discrete Event Systems

This article investigates quantitative supervisory control with local mean payoff objectives on discrete event systems modeled as weighted automata. Weight flows are generated as new events occur, which are required to satisfy some quantitative conditions. We focus on mean weights (payoffs) over a finite number of events, which serve as a measure for the stability or robustness of weight flows. The range of events to evaluate the mean payoff is termed a window, which slides as new events occur. Qualitative requirements such as safety and liveness are also necessary along with quantitative requirements. Supervisory control is employed to manipulate the operation of the system so that the requirements are satisfied. We consider two different scenarios based on whether the window size is fixed or not. Correspondingly, we formulate two supervisory control problems, both of which are solved sequentially by first tackling the qualitative issues and then the quantitative ones. The automaton model is then transformed to a two-player game between the supervisor and the environment, where safety and liveness are enforced. Based on the intermediate results, several quantitative objectives are defined to formulate two games, which correspond to the two proposed supervisory control problems. Finally, we synthesize provably correct supervisors by solving the games and completely resolve both problems.