Quantitative Supervisory Control Game for Discrete Event Systems

We formulate an optimal supervisory control problem for quantitative non-terminating discrete event systems (DESs) modeled by finite weighted automata. The control performance of a supervisor is evaluated by the worst-case limit-average weight of the infinite sequences generated by the supervised DES. An optimal supervisor is a supervisor that avoids deadlocks and maximizes the control performance. We propose a game theoretical design method for an optimal supervisor using a two-player turn-based mean-payoff game automaton. As the first player, the objective of the supervisor is to maximize the worst-case limit-average weight of the generated sequences; as the second player, the DES aims to minimize it. We show that an optimal supervisor can be computed from an optimal strategy (of the first player) for this game. Then, we propose an algorithm to compute an f-minimally restrictive optimal supervisor, which is a finite-memory optimal supervisor that enables as many sequences as possible and can be represented by an optimal strategy for a finite version of the two-player game.