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access icon free Linear programming-based robust model predictive control for positive systems

  • Author(s): Junfeng Zhang 1 ; Xudong Zhao 2 ; Yan Zuo 3 ; Ridong Zhang 3
    • View affiliations
    • Affiliations: 1: Institute of Information and Control, Automation, Hangzhou Dianzi University, Hangzhou 310018, People's Republic of China ;
      2: Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China ;
      3: Key Lab for IOT and Information Fusion Technology of Zhejiang, Hangzhou Dianzi University, Hangzhou 310018, People's Republic of China
  • Source: Volume 10, Issue 15, 10 October 2016, p. 1789 – 1797
    DOI:  10.1049/iet-cta.2016.0149 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 14/02/2016, Accepted 03/05/2016, Revised 07/04/2016, Published 13/06/2016

This study investigates the problem of robust model predictive control for positive systems under a new model predictive control framework. A robust model predictive control method is presented in this study for uncertain positive systems. A state-feedback control law that robustly stabilises the underlying system is designed by using linear programming. Different from the traditional model predictive control technique, the authors' proposed model predictive control framework employs a linear infinite horizon objective function and a linear Lyapunov function rather than quadratic performance indices and quadratic Lyapunov functions commonly used in the literature. Compared with existing design techniques for positive systems, the present approach owns the following advantages: (i) it gives a locally optimal control strategy which approaches to actual operation conditions and the control law is designed by solving a locally optimal control problem at each time step, (ii) it can explicitly deal with constraints of the systems, and (iii) the controller can be easily designed via linear programming without any additional constraints. An practical example is provided to verify the validity of the theoretical findings.

Inspec keywords: Lyapunov methods; linear programming; state feedback; uncertain systems; robust control; predictive control

Other keywords: system stability; locally optimal control strategy; state-feedback control law; linear Lyapunov function; uncertain positive systems; linear programming-based robust model predictive control; linear infinite horizon objective function

Subjects: Optimisation techniques; Stability in control theory; Optimal control

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