On Resilient Supervisory Control Against Indefinite Actuator Attacks in Discrete-Event Systems

In this letter we study a resilient supervisory control design problem in discrete-event systems. Consider that there are certain unsafe states in the system that must be prevented from entering, and this can be ensured by a supervisor disabling certain controllable events. Also consider that the system is subject to actuator attacks from intruders: some controllable events disabled by a supervisor may be re-enabled by an intruder. Our purpose is to address a challenging scenario where the controllable events that are vulnerable to attacks are indefinite, i.e., any controllable event can be attacked. Associating to each unsafe state with a required safety level (a positive integer), our aim of this letter is to design a resilient supervisor such that for every unsafe state $q$ , if the number of actuator attacks is no greater than the safety level of $q$ , then the controlled system is guaranteed to avoid entering $q$ . We first encode the behavior of the system under attack into an automaton called the resiliency automaton. We then show that the resilient supervisor synthesis problem may be cast into a supervisory control problem in the resiliency automaton. Hence, a maximally permissive resilient supervisor can be obtained by using the Ramadge-Wonham supervisory control paradigm. To the best of our knowledge, this is the first result on supervisory control design against indefinite actuator attacks in discrete-event systems.