Efficient model predictive control for Markovian jump systems with Lur'e nonlinear term: A dual‐mode control scheme

• Published in: International journal of robust and nonlinear control Vol. 32; no. 5; pp. 2603 - 2623
• Main Authors: Zhang, Bin, Song, Yan
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.03.2022
• Subjects: Algorithms; D C motors; efficient model predictive control; Electric motors; Feasibility; Feedback control; Lur'e‐type Lyapunov function; Markovian jump systems; nonlinear term; Optimization; Parameter uncertainty; Perturbation; Predictive control; Subsystems; terminal constraint set; Terminal constraints
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5844

In this article, the efficient model predictive control (MPC) problem is investigated for a class of Markovian jump Lur'e systems (MJLSs) subject to parameter uncertainties and input constraints, where each subsystem is described by the combination of a linear part and a nonlinear Lur'e term. The main purpose of the addressed problem is to design a set of dual‐mode feedback controllers in the framework of efficient MPC to make a nice tradeoff among the online computation burden, the initial feasible region, and the control performance. To this aim, the following two tasks need to be fulfilled: 1) for the terminal constraint set, the corresponding fixed feedback gain that is composed of a linear part and a nonlinear part is designed with aid of the Lur'e‐type Lyapunov‐like function related to the modes of subsystems; and 2) a fairly large initial feasible region is obtained off‐line by adjusting the dimension of the control perturbation sequence. Then, an online optimization problem is put forward to design this perturbation sequence with the determined dimension to steer the system state into the terminal constraint set within the pre‐determined steps. Sufficient conditions are presented to guarantee the recursive feasibility of the proposed efficient MPC algorithm and the mean‐square stability of the underlying MJLSs. Finally, a simulation example with regards to the DC motor device system is provided to demonstrate the effectiveness of our proposed MPC strategy.