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Mathematical Problems in Engineering
Volume 2014, Article ID 936093, 8 pages
Research Article

Off-Line Robust Constrained MPC for Linear Time-Varying Systems with Persistent Disturbances

1Department of Chemical Engineering, Faculty of Engineering, Mahidol University, Phuttamonthon 4 Road, Salaya, Nakhon Pathom 73170, Thailand
2Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Phayathai Road, Pathumwan, Bangkok 10330, Thailand

Received 13 November 2013; Revised 4 March 2014; Accepted 10 March 2014; Published 7 April 2014

Academic Editor: Driss Mehdi

Copyright © 2014 P. Bumroongsri and S. Kheawhom. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An off-line robust constrained model predictive control (MPC) algorithm for linear time-varying (LTV) systems is developed. A novel feature is the fact that both model uncertainty and bounded additive disturbance are explicitly taken into account in the off-line formulation of MPC. In order to reduce the on-line computational burdens, a sequence of explicit control laws corresponding to a sequence of positively invariant sets is computed off-line. At each sampling time, the smallest positively invariant set containing the measured state is determined and the corresponding control law is implemented in the process. The proposed MPC algorithm can guarantee robust stability while ensuring the satisfaction of input and output constraints. The effectiveness of the proposed MPC algorithm is illustrated by two examples.