Data driven secure control for cyber–physical systems under hybrid attacks: A Stackelberg game approach

This article presents a model-free Q-Learning algorithm for addressing the optimal control problem in cyber–physical systems (CPS) exposed to denial-of-service (DoS) attacks and false data injection (FDI) attacks. The problem is formulated as a non-cooperative game within the framework of the Stackelberg game, in which the control strategy acts as the leader, while the FDI attacks strategy serves as the follower. Guided by the principle of optimality, we derive the optimal control policy, which depends on the solution of an associated game algebraic Riccati equation (GARE). Moreover, we formulate adequate conditions ensuring the presence of a solution to the GARE. To locate this solution, we employ a Q-Learning algorithm, eliminating the necessity for knowledge of system dynamics and state. Ultimately, we provide simulation results that demonstrate the effectiveness of our proposed approach.