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Journal of Applied Mathematics
Volume 2012, Article ID 841609, 24 pages
Research Article

A Clustering and SVM Regression Learning-Based Spatiotemporal Fuzzy Logic Controller with Interpretable Structure for Spatially Distributed Systems

1Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronics and Automation, Shanghai University, Shanghai 200072, China
2School of Electrical Information and Automation, Qufu Normal University, Shandong 276826, China
3School of Control Science and Engineering, Shandong University, Jinan 250061, China

Received 8 April 2012; Revised 13 June 2012; Accepted 14 June 2012

Academic Editor: Baocang Ding

Copyright © 2012 Xian-xia Zhang 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.


Many industrial processes and physical systems are spatially distributed systems. Recently, a novel 3-D FLC was developed for such systems. The previous study on the 3-D FLC was concentrated on an expert knowledge-based approach. However, in most of situations, we may lack the expert knowledge, while input-output data sets hidden with effective control laws are usually available. Under such circumstance, a data-driven approach could be a very effective way to design the 3-D FLC. In this study, we aim at developing a new 3-D FLC design methodology based on clustering and support vector machine (SVM) regression. The design consists of three parts: initial rule generation, rule-base simplification, and parameter learning. Firstly, the initial rules are extracted by a nearest neighborhood clustering algorithm with Frobenius norm as a distance. Secondly, the initial rule-base is simplified by merging similar 3-D fuzzy sets and similar 3-D fuzzy rules based on similarity measure technique. Thirdly, the consequent parameters are learned by a linear SVM regression algorithm. Additionally, the universal approximation capability of the proposed 3-D fuzzy system is discussed. Finally, the control of a catalytic packed-bed reactor is taken as an application to demonstrate the effectiveness of the proposed 3-D FLC design.