Optimal supervisory control with mean payoff objectives and under partial observation

We investigate optimal mean payoff supervisory control problems on partially observed discrete event systems modeled as weighted finite-state automata. The event weights capture variations of a given resource (i.e., energy) expended or replenished during the operation of the system and the mean payoff is then defined as the average of the accumulative event weights. Two supervisory control problems are considered in this work. For the first, the system is equipped with a fixed amount of initial energy to support its operation and the supervised system should always have a nonnegative energy level. For the second, the limit mean payoff of any event sequence should never drop below zero in the supervised system. We further optimize the worst case limit mean payoff of infinite event sequences under both scenarios. The two problems are solved sequentially. In order to capture information on both the state estimate and the energy level of the system, we define energy information states which incorporate sufficient information for the decision making of the supervisor. Then we propose the First Cycle Energy Inclusive Controller (FCEIC) and further transfer the supervisory control problems into two-player games with properly defined objectives on the FCEIC. Finally, we perform a min–max search on the game graphs to synthesize the optimal supervisors for both scenarios.