Data-Driven Robust Control under Input-Output Stealthy Attacks

We consider the problem of robust control of an unknown but minimal linear time-invariant system under input and output disturbances and adversarial manipulation. An attacker can (i) corrupt sensor measurements (deception attacks) and (ii) perturb the control channel (actuation attacks). To address the lack of model knowledge, we adapt the Data-enabled Predictive Control (DeePC) framework, which constructs predictors directly from input–output data with bounded disturbance. We formulate a finite-horizon open-loop control problem as a two-player zero-sum game with asymmetric information: the defender selects control inputs based on measured data and only knows an upper bound on disturbances, whereas the attacker has access to the true disturbance realization and can remain stealthy by hiding within this uncertainty set. The main contributions are (i) sufficient conditions for the existence of a Nash equilibrium corresponding to saddle-point policies for this game, and (ii) an analysis of the defender’s security strategy against deception and actuation attacks. Simulation studies on finite-horizon control demonstrate the effectiveness of the proposed approach.