Finite-time control of discrete-time semi-Markov jump linear systems: A self-triggered MPC approach

• Published in: Journal of the Franklin Institute Vol. 359; no. 13; pp. 6939 - 6957
• Main Authors: He, Peng, Wen, Jiwei, Stojanovic, Vladimir, Liu, Fei, Luan, Xiaoli
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2022
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/j.jfranklin.2022.06.043

In this paper, a self-triggered model predictive control (MPC) strategy is developed for discrete-time semi-Markov jump linear systems to achieve a desired finite-time performance. To obtain the multi-step predictive states when system mode jumping is subject to the semi-Markov chain, the concept of multi-step semi-Markov kernel is addressed. Meanwhile, a self-triggered scheme is formulated to predict sampling instants automatically and to reduce the computational burden of the on-line solving of MPC. Furthermore, the co-design of the self-triggered scheme and the MPC approach is adjusted to design the control input when keeping the state trajectories within a pre-specified bound over a given time interval. Finally, a numerical example and a population ecological system are introduced to evaluate the effectiveness of the proposed control.