In this work, we propose and develop a new discrete-event based actuator attack model on the closed-loop system formed by the plant and the supervisor. We assume the actuator attacker partially observes the execution of the closed-loop system and eavesdrops the control commands issued by the supervisor. The attacker can modify each control command on a specified subset of attackable events. The attack principle of the actuator attacker is to remain covert until it can establish a successful attack and lead the attacked closed-loop system into generating certain damaging strings. We present a characterization for the existence of a successful attacker, via a new notion of attackability, and prove the existence of the supremal successful actuator attacker, when both the supervisor and the attacker are normal (that is, unobservable events to the supervisor cannot be disabled by the supervisor and unobservable events to the attacker cannot be attacked by the attacker). Finally, we present an algorithm to synthesize the supremal successful attackers that are represented by Moore automata.Keywords cyber-physical systems · discrete-event systems · supervisory control · actuator attack · partial observation IntroductionRecently, cyber-physical systems have drawn much research interest within the discreteevent systems and formal methods community [1]

In this paper, we propose and address the problem of supervisor obfuscation against actuator enablement attack, in a common setting where the actuator attacker can eavesdrop the control commands issued by the supervisor. We propose a method to obfuscate an (insecure) supervisor to make it resilient against actuator enablement attack in such a way that the behavior of the original closed-loop system is preserved. An additional feature of the obfuscated supervisor, if it exists, is that it has exactly the minimum number of states among the set of all the resilient and behavior-preserving supervisors. Our approach involves a simple combination of two basic ideas: 1) a formulation of the problem of computing behavior-preserving supervisors as the problem of computing separating finite state automata under controllability and observability constraints, which can be efficiently tackled by using modern SAT solvers, and 2) the use of a recently proposed technique for the verification of attackability in our setting, with a normality assumption imposed on both the actuator attackers and supervisors.

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In this work, we study the safety approach of synthesizing resilient supervisors against actuator attacks, for cyber-physical systems that can be modeled as discrete-event systems. A constraint based approach for the bounded synthesis of resilient supervisors is developed. The supervisor obfuscation problem, which is proposed in a specific setting of actuator attack, can be naturally modelled and solved using the same approach.