Modeling and Control of Discrete-Event Systems Under Joint Sensor–Actuator Cyberattacks

In this article, we investigate joint sensor–actuator cyberattacks in discrete-event systems. We assume that attackers can attack some sensors and actuators at the same time by altering observations and control commands. Because of the nondeterminism in observation and control caused by cyberattacks, the behavior of the supervised system becomes nondeterministic and may deviate from the safety specification. We define the upper bound on all possible languages that can be generated by the supervised system to investigate the safety supervisory control problem under cyberattacks. After introducing CA-controllability and CA-observability, we prove that the supervisory control problem under cyberattacks is solvable if and only if the given specification language is CA-controllable and CA-observable. Furthermore, we obtain methods to calculate the state estimates under sensor attacks and to synthesize a state-estimate-based supervisor to achieve a given safety specification under cyberattacks. We further show that of all the solutions, the proposed state-estimate-based supervisor is maximally permissive.