Dual-Optimization-Based Model Predictive Tracking Control of Semi-Markov Cyber–Physical Switch Systems Under DoS Attacks

This paper investigates the tracking optimiztion control problem of semi-Markov cyber-physical switch systems under denial of service (DoS) attacks. Firstly, given the complexity and randomness of the network, the DoS attacks and the modal switching dynamics are modeled as Markov and semi-Markov stochastic processes with dwell time following arbitrary distributions, respectively. By introducing mode-dependent reference transition variables, a predictive tracking model of the semi-Markov cyber-physical systems is constructed under the influence of external reference inputs. A robust model predictive control scheme based on stabilizing and tracking optimization problems are formulated. By combining Lyapunov stability analysis with cost function, and utilizing invariant set theory and matrix elimination techniques, solvable σ-error mean-square stability conditions are derived over the entire switching period and the discrete-time domain. Finally, two examples demonstrate the effectiveness of the proposed control approach.