Fault-Tolerant Control of Discrete-Event Systems with Controllability Failures

A supervisory policy controls a Discrete-Event System (DES) by appropriately disabling a subset of events, known as controllable events, based on the observed event string generated by the supervised DES thus far. We consider supervisory control of DES in the presence of an extraneous fault that renders an arbitrary subset of controllable events to be temporarily uncontrollable. The fault is detected at the first occurrence of a controllable event that was disabled by the supervisor. It is rectified after finitely-many such unintended occurrences of controllable events following which the supervisor regains control of all controllable events and can prevent them from occurring when deemed necessary. We present a necessary and sufficient condition for the existence of a supervisor that enforces a desired language specification in the paradigm of Ramadge and Wonham, under the fault semantics described above. We also prove that such a supervisor, if it exists, can always be synthesized if the language of the plant and the specification is regular.