Output-feedback Linear Quadratic Robust Control under Actuation and Deception Attacks

We consider output-feedback robust control of a linear system subject to disturbances and noise and in presence of an attacker who: 1) can corrupt the measured output (deception attack) and, 2) can introduce perturbations to the control signal (actuation attack). We consider an open-loop control problem over a finite horizon which models the scenario where feedback control could be stopped if one is certain that an attack is ongoing. We formulate this problem as a zero-sum game between a defender that selects the control signal based on a measured output and an attacker that selects the attack signals. The game has asymmetric information in that the defender only knows the measured output, whereas the attacker knows additional information, which includes the value of initial conditions and disturbances/measurement noise. The main contributions are (i) sufficient conditions for the existence of a Nash equilibrium corresponding to a saddle-point for the defender and (ii) a computationally efficient procedure to compute a pair of policies that form a Nash equilibrium for the game. We apply the procedure to a finite horizon linear quadratic control problem.