Finite‐Time Sliding Mode Resilient Control for Discrete‐Time Singular Perturbation Markov Jump CPSs Under Deception Attacks and Actuator Failures

Abstract

This paper addresses the control challenges for discrete‐time singularly perturbed Markov jump cyber‐physical systems (CPSs) under deception attacks, actuator failures, and limited network bandwidth. A novel asynchronous sliding mode control (SMC) strategy is proposed, and it integrates finite‐time convergence with actuator fault tolerance. First, a novel probabilistic dynamic event‐triggered mechanism is designed. By using probabilistic decision‐making and dynamic auxiliary variables, it overcomes the conservatism of traditional triggers in stochastic networks and significantly reduces communication overhead. Second, deception attacks and actuator failures are considered at the same time. Deception attacks are described by Bernoulli distributions, and actuator failures are modeled by multiplicative uncertainties. This makes the system model closer to real working conditions. Third, an asynchronous control framework is established, and the co‐design of controller gains and event‐triggered weighting matrices is achieved. Controller modes and system modes are not synchronized, and they are linked by a conditional probability matrix. Moreover, sufficient conditions for singular perturbation finite‐time boundedness (SPFTB) with performance are given for both the reaching phase and the sliding motion phase. These conditions are presented as linear matrix inequalities (LMIs) and can be solved directly by MATLAB. Finally, numerical simulations on petroleum catalytic cracking processes verify the effectiveness and practicality of the proposed method.