Optimal Consensus Control Strategy for Multi-Agent Systems Under Cyber Attacks via a Stackelberg Game Approach

Based on the Stackelberg game theory, this paper studies the optimal consensus control problem of the multi-agent system (MAS) under multiple network attacks. Multiple attackers interfere with the information interaction between agents by intervening in the transmission channel of the multi-agent wireless network, thereby changing the communication topology of the MAS. Under the limited energy of the system and attackers, the energy allocation of transmission channels is used as the performance index, and the importance of the transmission channel to the MAS is used as an auxiliary indicator to establish a Stackelberg game model between the MAS and attackers under incomplete information. By solving the Stackelberg equilibrium solution of the game model, the optimal attack energy allocation scheme and the optimal energy allocation scheme of the system are obtained, respectively. Then, based on the equilibrium solution, the Hamilton-Jacobi-Bellman equation with coupling terms for the MAS under attacks is given. In view of the broad learning system theory, online algorithms that approximate the optimal performance function and the optimal controller are designed respectively, and sufficient conditions are obtained for the proposed optimal controller to ensure the stability and consistency of the MAS. Finally, the effectiveness of the method is verified by a numerical simulation. Note to Practitioners— This study employs a Stackelberg game model to analyze the optimal consensus control problem in the MAS facing network attacks. By utilizing this framework, effective energy allocation strategies can be devised for both the MAS and potential attackers under resource constraints, demonstrating broad applicability across various fields, including intelligent vehicle fleets and power grids. The simulation section specifically focuses on the attack-defense dynamics of autonomous aerial vehicles, validating energy allocation strategies and control algorithms under different attack scenarios, thus providing effective solutions for real-world applications.