Framework for Optimal Fault-Tolerant Control Synthesis: Maximize Prefault While Minimize Post-Fault Behaviors

In an earlier work, we introduced a framework for fault-tolerant supervisory control of discrete event systems and presented a necessary and sufficient condition for its existence. In this paper, we introduce the synthesis of an optimal fault-tolerant supervisory controller. Given a discrete event plant with both post-fault and prefault behaviors, an optimal fault-tolerant supervisor we synthesize enforces a set of behaviors in which: 1) a recovery is guaranteed within a bounded delay following any fault; 2) all safety and nonblocking properties are satisfied; 3) the enforced set of prefault behaviors is maximized, and 4) a minimal set of post-fault behaviors is tolerated to achieve recovery in a minimal number of steps. An optimal solution requires a simultaneous maximization (of prefault behaviors) and minimization (of post-fault and prerecovery behaviors), which is quite novel. The optimal solution further minimizes the delay of recovery. The computation has complexity quadratic in the size of plant.