Supervisory control of Petri nets with uncontrollable and unobservable transitions under replacement attacks

In this paper, we study the robust control of discrete event systems modeled by Petri nets with uncontrollable and unobservable transitions under replacement attacks. The existing supervisory control methods for discrete event systems modeled as Petri nets under replacement attack can only deal with the systems with observable and controllable transitions, and cannot deal with the systems with unobservable and uncontrollable transitions. Three methods are proposed in this paper to prevent the system from reaching illegal markings by disabling some controllable transitions according to a generalized mutual exclusion constraint. These methods can deal with Petri nets containing transitions that are not observed or controlled. The proposed framework provides a versatile range of strategies, from optimal control policies for high-precision requirements to efficient structural algorithms suitable for large-scale systems. It effectively mitigates the impact of replacement attacks while ensuring rigorous system safety. By extending Petri net supervisors to compromised environments with incomplete information, this work establishes a robust theoretical foundation for securing complex industrial discrete event systems.