Synthesis of Optimal Multiobjective Attack Strategies for Controlled Systems Modeled by Probabilistic Automata

In this article, we study the security of control systems in the context of the supervisory control layer of stochastic discrete-event systems. Control systems heavily rely on correct communication between the plant and the controller. In this article, we consider that such communication is partially compromised by a malicious attacker. The attacker has the ability to modify a subset of the sensor readings and mislead the supervisor, with the goal of inducing the system into an unsafe state. We consider this problem from the attacker’s viewpoint and investigate the synthesis of an attack strategy for systems modeled as probabilistic automata. Specifically, we investigate the synthesis of attack functions constrained by multiple objectives. We proceed in two steps. First, we quantify each attack strategy based on the likelihood of successfully reaching an unsafe state. Based on this quantification, we study the problem of synthesizing attack functions with the maximum likelihood of successfully reaching an unsafe state. Second, we consider the problem of synthesizing attack functions that have the maximum likelihood of successfully reaching an unsafe state while minimizing a cost function, i.e., the synthesis of attack functions is constrained by multiple objectives. Our solution methodology is based on mapping these problems to optimal control problems for Markov decision processes, specifically, a probabilistic reachability problem and a stochastic shortest path problem.