Two classes of B-spline fuzzy systems and their applications
两类B样条模糊系统及其应用

Fuzzy systems that approximate a given function and its derivatives play an important role in applications. Two classes of B-spline fuzzy systems that employ B-spline functions as the if-part sets are presented. They are universal approximators for a given function and its derivatives. Especially, the first class of B-spline fuzzy systems with the interpolation condition can approximate a function and its derivative respectively with the 2nd order accuracy and the 1st order accuracy in the approximation, The second class of B-spline fuzzy systems with the quasi-interpolation condition can approximate a function and its first and second derivatives with the 2nd order accuracy for all. Finally, a controller based on the two fuzzy systems is designed to realize the stability for a 1st order single inverted pendulum. The simulation results demonstrate the effectiveness and robustness of the controller based on the proposed fuzzy systems.