Critic-only adaptive dynamic programming algorithms' applications to the secure control of cyber-physical systems

Industrial cyber-physical systems generally suffer from the malicious attacks and unmatched perturbation, and thus the security issue is always the core research topic in the related fields. This paper proposes a novel intelligent secure control scheme, which integrates optimal control theory, zero-sum game theory, reinforcement learning and neural networks. First, the secure control problem of the compromised system is converted into the zero-sum game issue of the nominal auxiliary system, and then both policy-iteration-based and value-iteration-based adaptive dynamic programming methods are introduced to solve the Hamilton-Jacobi-Isaacs equations. The proposed secure control scheme can mitigate the effects of actuator attacks and unmatched perturbation, and stabilize the compromised cyber-physical systems by tuning the system performance parameters, which is proved through the Lyapunov stability theory. Finally, the proposed approach is applied to the Quanser helicopter to verify the effectiveness.