Bayesian-Stackelberg-Game-Based Finite-Time Sliding Mode Fault-Tolerant Secure Control for Cyber–Physical Systems Under Jamming Attacks and Multiple Physical Faults

This article investigates the sliding mode fault-tolerant secure control for cyber-physical system facing jamming attacks and multiple physical faults. An intelligent attacker is capable of emitting interference power and adjusting its strategy by observing the transmitter's sending power, leading to packet dropouts in the controller-to-actuator channel. A Bayesian Stackelberg game is exploited to capture these competitive interactions between the two players, in which the transmitter and the intelligent attacker can only probabilistically obtain information about each other's channel state and transmission cost. Meanwhile, the transmitter has only statistical knowledge about either the presence or absence of the attacker in the practical environment. First, optimal transmission power strategies for both sides are studied using the backward induction method and the Karush-Kuhn-Tucker condition. Second, an integrated observer is designed to simultaneously estimate the system state, actuator fault, and sensor fault. Furthermore, the reaching law is proposed so that the state trajectories can reach the preselect sliding surface during the assigned finite time interval from any initial state. Sufficient criteria are derived to guarantee stochastic finite-time boundedness during reaching and sliding motion phases of closed-loop systems using a sliding-mode fault-tolerant secure controller. Finally, simulation results validate the effectiveness and superiority of the proposed method.