Co-design of transition rates and sliding mode switched controller for Markovian jumping systems under intermittent DoS attacks

• Published in: Journal of the Franklin Institute Vol. 359; no. 8; pp. 3549 - 3574
• Main Authors: Chen, Bei, Jia, Tinggang, Niu, Yugang
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.05.2022; Elsevier Science Ltd
• Subjects: Algorithms; Closed loop systems; Co-design; Controllers; Denial of service attacks; Dynamic stability; Feedback control; Intermittent denial-of-service attacks; Liapunov functions; Markovian jump systems; Optimization; Optimization algorithms; Sliding friction; Sliding mode control; Stability analysis; Switching; Synchronous/asynchronous switching strategy; Synthesis; Systems stability; Transition rate synthesis; Synchronous/asynchronous switching strategy; Markovian jump systems; Co-design; Transition rate synthesis; Intermittent denial-of-service attacks; Sliding mode control
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2022.03.015

This paper focuses on the stabilization problem for a class of Markovian jumping systems (MJSs) subject to intermittent denial-of-service (IDoS) attacks by synthesizing the sliding mode control (SMC) and the transition rate matrix (TRM). The existing conditions for the transition rates are firstly established to ensure the exponential mean-square stability of the unforced uncertain MJSs. And then, a co-design scheme for both the sliding mode controller and TRM is synthesized to achieve the exponential mean-square stability of the closed-loop system under IDoS, in which a switching estimator is utilized to estimate the unmeasurable system state. By introducing a novel Lyapunov function, both the reachability and the stability of sliding mode dynamics are detailedly analyzed, and an iterative optimization algorithm is given for solving the corresponding sufficient conditions. Finally, the proposed co-design SMC strategy is illustrated via the simulation examples.