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Robust constrained model predictive control based on parameter-dependent Lyapunov functions

Xia, Yuanqing and Liu, Guo-Ping and Shi, Peng and Cheng, Jie and Rees, David (2008) Robust constrained model predictive control based on parameter-dependent Lyapunov functions. Circuits Systems and Signal Processing, 27 (4). pp. 429-446. ISSN 0278-081X

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Abstract

The problem of robust constrained model predictive control (MPC) of systems with polytopic uncertainties is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques.

Item Type: Article
Uncontrolled Keywords: ResPubID18741, MPC, robust control, polytopic uncertainty, stability, optimization, LMI
Subjects: Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
FOR Classification > 0199 Other Mathematical Sciences Information Systems
Depositing User: VUIR
Date Deposited: 08 Jun 2011 05:25
Last Modified: 19 Mar 2015 04:55
URI: http://vuir.vu.edu.au/id/eprint/4063
DOI: 10.1007/s00034-008-9036-9
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Citations in Scopus: 16 - View on Scopus

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