Zero-Sum Game-Based Optimal Estimation–Compensation Control for Multi-Agent Systems Under Hybrid Attacks

This article develops a zero-sum game-based optimal estimation compensation scheme for multi-agent systems under denial-of-service (DoS) attacks and false data injection (FDI) attacks. First, a unified observer is developed to observe consensus error under the FDI attack and the DoS attack. Second, a FDI secondary compensator (FDI-SC) for the FDI attack is designed to compensate for the unestimated state of the FDI attack estimated by the unified observer and consensus deviations. Third, an integral reinforcement learning (IRL) algorithm is introduced to address the difficulty of computing the unknown FDI-related states. Additionally, the unified observer and FDI-SC are modeled as participants in a zero-sum game, which is integrated with the DoS attack model within the IRL framework to obtain an optimal solution. Finally, the stability conditions are established based on the Hamilton-Jacobi-Bellman and Lyapunov-Krasovskii methods. The simulation results demonstrate the effectiveness of this method.