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In this work, we investigate how to make use of model reduction techniques toidentify the vulnerability of a closed-loop system, consisting of a plant and asupervisor, that might invite attacks. Here, the system vulnerability refers tothe existence of key observation sequences that could be exploited by aspecific smart sensor attack to cause damage infliction. We consider anondeterministic smart attack, i.e., there might exist more than one attackchoice over each received observation, and adopt our previously proposedmodeling framework, where such an attack is captured by a standard finite-stateautomaton. For a given supervisor S and a smart sensor attack model A, anothersmart attack model A' is called attack equivalent to A with respect to S, ifthe resulting compromised supervisor, defined as the composition of thesupervisor S and attack model A', is control equivalent to the originalcompromised supervisor, defined as the composition of S and A. Following thespirit of supervisor reduction that relies on the concept of controlcongruence, we will show that, this problem of synthesizing a reduced smartattack model A' that is attack equivalent to A with respect to S, can betransformed to a classical supervisor reduction problem, making all existingsynthesis tools available for supervisor reduction directly applicable to ourproblem. A simplified and ideally minimum-state attack model can reveal allnecessary observation sequences for the attacker to be successful, thus,reminds system designers to take necessary precautions in advance, which mayimprove system resilience significantly. An example is presented to show theeffectiveness of our proposed attack model reduction technique to identify thesystem vulnerability.

Identification of System Vulnerability under a Smart Sensor Attack via Attack Model Reduction