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

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. (c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

In this paper, a self-triggered model predictive control (MPC) strategy is proposed for discrete-time semi-Markov jump linear systems to achieve a desired finite-time performance. By introducing the concept of multi-step semi-Markov kernel, the multi-step predictive states under system mode jumping are obtained. Meanwhile, a self-triggered scheme is used to automatically predict sampling instants and reduce the computational burden of on-line solving of MPC.