Faired MISO B-Spline Fuzzy Systems and Its Applications

Abstract

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.

Fuzzy B-Spline Surface Modeling

“…Although both methods employed fuzzification phase, it is still in interval surface form which is not in single surface form. Furthermore, the fuzzification and defuzzification process of B-spline fuzzy system [19] were not elaborated in detail. Therefore, this paper elucidates defuzzification process upon the application of fuzzification process.…”