Persuasion-Based Robust Sensor Design against Attackers with Unknown Control Objectives

We introduce a robust sensor design framework to provide 'persuasion-based' defense in stochastic control systems against an unknown type attacker with a control objective exclusive to its type. We design a robust 'linear-plus-noise' signaling strategy in order to persuade the attacker to take actions that lead to minimum damage with respect to the system's objective. The specific model we adopt is a Gauss-Markov process driven by a controller with a (partially) 'unknown' malicious/benign control objective. We seek to defend against the worst possible distribution over control objectives in a robust way under the solution concept of Stackelberg equilibrium, where the sensor is the leader. We show that a necessary and sufficient condition on the covariance matrix of the posterior belief is a certain linear matrix inequality. This enables us to formulate an equivalent tractable problem, indeed a semidefinite program, to compute the robust sensor design strategies 'globally' even though the original optimization problem is nonconvex and highly nonlinear. We also extend this result to scenarios where the sensor makes noisy or partial measurements.