利用模糊神經網路計算未知函數的偏微分

Abstract

在本論文中，我們使用一個模糊神經網路去近似一個未知函數，並求 其偏微分值。既然這個模糊神經網路能夠近似任意連續函數，而且當它的 歸屬函數都可以微分時，那它也必然可以微分。所以我們利用這個模糊神 經網路的偏微分去取代這個未知函數的偏微分。在這個模糊神經網路的架 構中，我們只要改變它的歸屬函數便可輕易的得到它的任意階的微分。一 般而言，少量的函數誤差可能導致相當大的微分誤差，基於實用和方便分 析的考量，我們提出一個簡單且實用的技巧來消除此一現像。最後，我們 將這個方法應用到最佳化問題及適應性控制 (adaptive control)問題。 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.