Mean Payoff Supervisory Control under Partial Observation

The problem under investigation is mean payoff supervisory control on a partially observed quantitative discrete event system modeled by a finite state weighted automaton. We intend to design a partial-observation supervisor such that the limit-average weights of all infinite sequences in the supervised system remain nonnegative. This problem may be viewed as a two-player quantitative game between the supervisor and the environment, with asymmetric information and a mean payoff objective. To cope with partial observation of the supervisor, we introduce the energy information state which incorporates information about both state estimate and energy change for supervisor's decision making. Based on that, we transfer the supervisory control problem into a two-player reachability game under full observation and propose a finite bipartite structure called First Cycle Energy Inclusive Controller (FCEIC). Further analysis demonstrates that winning strategies in the FCEIC lead to solutions to the original control problem.