Constrained robust model predicted control of discrete-time Markov jump linear systems

• Published in: IET control theory & applications Vol. 13; no. 4; pp. 517 - 525
• Main Authors: Lopes, Rosileide O, Mendes, Eduardo M. A. M, Torres, Leonardo A. B, Palhares, ReinaldoM
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 05.03.2019
• Subjects: control system synthesis; discrete time systems; discrete‐time Markov jump linear systems; linear matrix inequalities; linear matrix inequality conditions; linear systems; LMI; Markov processes; model predictive control; MPC; multistep mode‐dependent state‐feedback control design; predictive control; Research Article; robust control; robust model; state feedback; stochastic systems; transition probability; uncertain system; uncertain systems; model predictive control; MPC; transition probability; discrete time systems; uncertain systems; discrete-time Markov jump linear systems; multistep mode-dependent state-feedback control design; robust model; control system synthesis; linear matrix inequality conditions; uncertain system; LMI; linear systems; linear matrix inequalities; Markov processes; stochastic systems; robust control; state feedback; predictive control
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2018.5543

This study is concerned with the problem of designing a robust model predictive control (MPC) for a class of uncertain discrete-time Markov jump linear systems. The main contribution is a set of linear matrix inequality (LMI) conditions obtained under new control policies for the unconstrained as well as the constrained MPC when uncertainties are present both in the system's matrices and in the transition probabilities of the modes. For the constrained MPC, hard constraints are considered over the input control and the states and results are extended to the so-called multi-step mode-dependent state-feedback control design. To illustrate the improvements obtained with the new set of LMI conditions, numerical simulations are carried out and compared with a recent reference in the literature.