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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 982041, 10 pages
Research Article

Fast Model Predictive Control Combining Offline Method and Online Optimization with K-D Tree

National Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China

Received 26 April 2015; Revised 5 July 2015; Accepted 22 July 2015

Academic Editor: Jean J. Loiseau

Copyright © 2015 Yi Ding et al. 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.


Computation time is the main factor that limits the application of model predictive control (MPC). This paper presents a fast model predictive control algorithm that combines offline method and online optimization to solve the MPC problem. The offline method uses a k-d tree instead of a table to implement partial enumeration, which accelerates online searching operation. Only a part of the explicit solution is stored in the k-d tree for online searching, and the k-d tree is updated in runtime to accommodate the change in the operating point. Online optimization is invoked when searching on the k-d tree fails. Numerical experiments show that the proposed algorithm is efficient on both small-scale and large-scale processes. The average speedup factor in the large-scale process is at least 6, the worst-case speedup factor is at least 2, and the performance is less than 0.05% suboptimal.