Game-theoretic tracking control for actuator attack attenuation in cyber-physical systems

In this paper a game-theoretic adaptive learning algorithm based on an action-dependent value function (Q-function) is proposed to solve the optimal tracking control problem with adversarial inputs and completely unknown system and reference dynamics. In order to convert the tracking problem to a regulation problem we augment the system and the reference states and pick appropriately the user-defined matrices. An integral reinforcement learning approach is used to estimate the parameters of the Q-function while also guaranteeing closed-loop stability, trajectory tracking and convergence of the policies to a saddle point. A simulation result of a Quanser helicopter shows the efficacy of the proposed approach.