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This article considers the problem of risk-optimal allocation of securitymeasures when the actuators of an uncertain control system are under attack. Weconsider an adversary injecting false data into the actuator channels. Theattack impact is characterized by the maximum performance loss caused by astealthy adversary with bounded energy. Since the impact is a random variable,due to system uncertainty, we use Conditional Value-at-Risk (CVaR) tocharacterize the risk associated with the attack. We then consider the problemof allocating the security measures which minimize the risk. We assume thatthere are only a limited number of security measures available. Under thisconstraint, we observe that the allocation problem is a mixed-integeroptimization problem. Thus we use relaxation techniques to approximate thesecurity allocation problem into a Semi-Definite Program (SDP). We also compareour allocation method $(i)$ across different risk measures: the worst-casemeasure, the average (nominal) measure, and $(ii)$ across different searchalgorithms: the exhaustive and the greedy search algorithms. We depict theefficacy of our approach through numerical examples.

Risk-based Security Measure Allocation Against Injection Attacks on Actuators