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Mathematical Problems in Engineering
Volume 2013, Article ID 870595, 9 pages
Research Article

Faired MISO B-Spline Fuzzy Systems and Its Applications

1Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China
2School of Sciences, Hebei University of Technology, Tianjin 300130, China

Received 11 December 2012; Accepted 7 February 2013

Academic Editor: Wudhichai Assawinchaichote

Copyright © 2013 Tan Yanhua and Li Hongxing. 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.


We construct two classes of faired MISO B-spline fuzzy systems using the fairing method in computer-aided geometric design (CAGD) for reducing adverse effects of the inexact data. Towards this goal, we generalize the faring method to high-dimension cases so that the faring method only for SISO and DISO B-spline fuzzy systems is extended to fair the MISO ones. Then the problem to construct a faired MISO B-spline fuzzy systems is transformed into solving an optimization problem with a strictly convex quadratic objective function and the unique optimal solution vector is taken as linear combination coefficients of the basis functions for a certain B-spline fuzzy system to obtain a faired MISO B-spline fuzzy system. Furthermore, we design variable universe adaptive fuzzy controllers by B-spline fuzzy systems and faired B-spline fuzzy systems to stabilize the double inverted pendulum. The simulation results show that the controllers by faired B-spline fuzzy systems perform better than those by B-spline fuzzy systems, especially when the data for fuzzy systems are inexact.