Computing the Partial Derivatives of an Unknown Function Using Fuzzy Network

• Main Authors: Tseng, Chun-Ren, 曾俊仁
• Other Authors: Ching-Cheng Teng
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/98850716449115161338

碩士 === 國立交通大學 === 控制工程系 === 84 === In this thesis, we use a fuzzy neural network (FNN) system to approximatelycompute the partial derivative of an unknown function. Since the FNN is a universal approximator and is differentiable when its membership functions areall differentiable, we will use its partial derivatives to substitute the partial derivatives of an unknown function. From the proposed FNN structure, the derivative of any order can be easily obtained by only changing its membership functions. As we know, a slight modeling error may cause a large sensitivity error. This error is reduced by canceling the redundant rules which are negligible on the function value but are important on the derivative. Furthermore, this proposed method is also illustrated by solving an optimization problem and obtaining the sensitivity of the unknown system on adaptive control.