Design of robust supervisors for prefix-closed language specifications

We study the issue of robustness of supervisors for discrete event systems. The control objective is to synthesize a supervisor such that the closed-loop behavior lies within a prespecified range whose lower and upper bounds are given as prefix-closed languages. In general, there exists more than one supervisor which satisfies the specification for the nominal plant. We first synthesize the most robust supervisor which maximizes the set of plants for which the specification is satisfied under the supervision. However, the most robust supervisor may be restrictive for the nominal plant, and one may want a more permissive supervisor for the nominal plant at the price of robustness. We characterize the performance of a supervisor in terms of permissiveness for the nominal plant and robustness. We then present techniques to improve each of these two performance measures for a given supervisor