Stackelberg-Game-Based Sliding Mode Fault-Tolerant Secure Control for Cyber-Physical Systems Against Jamming Attacks and Multiple Physical Intermittent Faults

This paper investigates the sliding mode fault-tolerant secure control issue for cyber-physical systems under both cyber jamming attacks and multiple physical intermittent faults. A Stackelberg game is used to model the competitive interaction between the transmitter and the attacker, where the attacker is intelligent enough to observe the sending power of the transmitter and adaptively adjust its interference power accordingly. The best transmission power strategies for both sides are investigated by taking into account energy constraints and observation errors. To quantify the impact of jamming attacks on the system, the Gilbert-Elliott model is adopted to describe the attack-induced packet dropout process and characterize the correlation among packet dropouts. Additionally, an integrated observer is designed for simultaneous estimation of the system state, actuator intermittent fault, and sensor intermittent fault. Then, the Stackelberg-game-based sliding mode fault-tolerant secure controller is designed based on the estimated information, which can force the sliding dynamic onto the pre-set sliding mode region. Afterward, sufficient conditions are derived to ensure the asymptotic stability of the closed-loop system with guaranteed $H_{\infty }$ performance. Finally, the effectiveness of the proposed sliding mode fault-tolerant secure control scheme is verified by a numerical example.