Supervisory Control for Stabilization under Multiple Local Average Payoff Constraints

This work investigates stabilization of discrete event systems via supervisory control under a series of quantitative constraints. Every event in the system model is weighted by a vector which represents payoffs of quantitative variables associated by the event. Multidimensional weight flows are generated when events occur successively. The supervisor aims to drive the generated strings to a reach set of target states to stabilize the system. Meanwhile, the supervisor is also responsible for regulating the weight flows so as to guarantee that at each dimension, the average weight every a certain number of events does not fall below a given threshold. Next, the formulated supervisory control problem is transformed to a two-player game between the supervisor and the environment on a specially defined game structure. Then we specify the objective of the game and synthesize game winning supervisors, which turn out to provably solve the proposed problem.