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.
Highlights
Since Zadeh introduced fuzzy theory in 1965, fuzzy systems have been utilized successfully in many areas, such as fuzzy control, classification, expert systems, and others
We propose a regularization term taken as the energy function of the MISO B-FS
The two classes of MISO B-FSs we proposed in [12, 13]
Summary
Since Zadeh introduced fuzzy theory in 1965, fuzzy systems have been utilized successfully in many areas, such as fuzzy control, classification, expert systems, and others. We construct two classes of faired B-spline fuzzy systems (faired B-FSs) to reduce adverse effects of the inexact I/O data on fuzzy systems as well as improve their performance. For faring these two classes of B-FSs, the energy extremum principle (energy method) based faring method in CAGD is utilized for its overall modification nature. We note that the energy method in CAGD is only used to fair curves and surfaces, which means it can only fair the SISO and DISO B-FSs. So, we propose a regularization term taken as the energy function of the MISO B-FS.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
