两类B样条模糊系统及其应用

能够同时逼近函数及其导函数的模糊系统在应用中具有重要意义.本文利用B样条函数作为推理前件,得到了两类能够同时逼近函数及其导函数的B样条模糊系统.其中第一类B样条模糊系统是插值系统且对函数及其一阶导函数分别具有二阶和一阶逼近精度,第二类B样条模糊系统是拟插值系统且对函数及其一阶、二阶导函数均具有二阶逼近精度.最后,将这两类模糊系统应用到一级倒立摆的稳定控制中,仿真结果表明利用这两类模糊系统设计的控制器是可行的,且具有一定的鲁棒性.

Two classes of B-spline fuzzy systems and their applications

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.