Stackelberg game-based robust optimal control of cyber-physical system under hybrid attacks

This paper presents a novel framework integrating Stackelberg game theory and reinforcement learning for cyberphysical system (CPS) security. We develop a hierarchical game model where defenders and attackers interact through sequential decision-making. The defender-attacker dynamics are formulated as an optimization problem combining H2 and H∞ control objectives. Key innovations include: 1) A unified game-theoretic approach for modeling hybrid attack-defense mechanisms, 2) Online reinforcement learning algorithms for real-time strategy adaptation, and 3) Rigorous stability analysis using Lyapunov theory. Theoretical guarantees of convergence are established for the proposed learning scheme. Comprehensive experiments on a robotic platform validate the framework’s effectiveness in maintaining control performance under diverse attack scenarios.

Recommended citation: Tan, Jun Kai and Xue, Shuang Si and Cao, Hui (2025). Stackelberg game-based robust optimal control of cyber-physical system under hybrid attacks. The International Journal of Intelligent Control and Systems.