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Journal of Applied Mathematics
Volume 2013, Article ID 410279, 13 pages
Research Article

Reference Function Based Spatiotemporal Fuzzy Logic Control Design Using Support Vector Regression Learning

Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronics and Automation, Shanghai University, Shanghai 200072, China

Received 25 August 2013; Accepted 1 November 2013

Academic Editor: Baocang Ding

Copyright © 2013 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.


This paper presents a reference function based 3D FLC design methodology using support vector regression (SVR) learning. The concept of reference function is introduced to 3D FLC for the generation of 3D membership functions (MF), which enhance the capability of the 3D FLC to cope with more kinds of MFs. The nonlinear mathematical expression of the reference function based 3D FLC is derived, and spatial fuzzy basis functions are defined. Via relating spatial fuzzy basis functions of a 3D FLC to kernel functions of an SVR, an equivalence relationship between a 3D FLC and an SVR is established. Therefore, a 3D FLC can be constructed using the learned results of an SVR. Furthermore, the universal approximation capability of the proposed 3D fuzzy system is proven in terms of the finite covering theorem. Finally, the proposed method is applied to a catalytic packed-bed reactor and simulation results have verified its effectiveness.