Reinforcement learning based sliding mode control for two-time-scale multi-agent systems with malicious attacks

Abstract

The optimal consensus problem for linear two-time-scale multi-agent systems under malicious attacks is studied in this paper. Firstly, an integral sliding mode function is devised to guide the system trajectory towards the sliding mode surface and the impact of attacks can be eliminated. Then, the optional consensus problem is reformulated as a zero-sum game problem between each agent and its neighbouring agents. Thus, the game algebraic Riccati equation with singularly perturbed parameter is formulated. Furthermore, to avoid the requirement of the system dynamics information, an integral reinforcement learning algorithm is presented to obtain the optimal control policy for multi-agent systems. Compared with existing learning methods, the obtained reinforcement learning algorithm is devoid of potential calculation error issues from singularly perturbed parameter. Meanwhile, the convergence of the proposed algorithm is verified. Finally, a simulation example is provided to demonstrate the efficacy of the proposed control method.