📄 17.htm
字号:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<!-- saved from url=(0042)http://www.jgchina.com/ednns/ednnsbk/7.htm -->
<HTML><HEAD><TITLE>第四章 神经模糊控制</TITLE>
<META http-equiv=Content-Type content="text/html; charset=gb2312">
<META content="MSHTML 6.00.2800.1106" name=GENERATOR>
<META content=FrontPage.Editor.Document name=ProgId><LINK
href="17.files/style.css" type=text/css rel=stylesheet></HEAD>
<BODY bgColor=#ffffff leftMargin=0 topMargin=0>
<TABLE height=1755 cellSpacing=0 cellPadding=0 width=778 border=0>
<TBODY>
<TR>
<TD width="100%" height=17>
<P><A
href="http://www.jgchina.com/ednns/ednnsbk/director.htm">回目录</A>
<A
href="http://www.jgchina.com/ednns/ednnsbk/6.3.3.htm">上一页</A>
<A href="http://www.jgchina.com/ednns/ednnsbk/7.2.htm">下一页</A> </P></TD></TR>
<TR>
<TD width="100%" height=8>
<P align=center>第四章 神经模糊控制</P></TD></TR>
<TR>
<TD width="100%" height=105>
<P>用神经网络去实现模糊控制则称为神经模糊控制(Neuro-Fuzzy
Control)。神经模糊控制是神经网络应用的一个重要方向。这种控制最吸引人的是能够对神经网络进行学习，从而可对模糊控制系统实现优化。 </P>
<P>神经模糊控制有两种不同的实现方法。一种是用常规神经元和模糊神经元组成网络实现模糊控制；另一种是用模糊神经元组成网络实现控制。</P>
<P>模糊神经网络FNN3是典型的网络，Buckley等人证明了FNN3是一种单调映射，故而FNN3不是通用逼近器，但混合模糊神经网络HFNN则是通用逼近器。</P>
<P>模糊控制的控制曲面具有单调的特征，所以，模糊神经网络可以用于模糊控制。模糊控制中较多采用Mamdani以及Takagi-Sugeno推理。对于Mamdani推理，控制规则形式为：</P>
<P>Ri：if x is Ai and y is Bi then Z is Ci每条规则的击发强度为：</P>
<P><SPAN
style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">α</SPAN><SUB>i</SUB>=μ<SUB>Ai</SUB>(X<SUB>0</SUB>)Λμ<SUB>Bi</SUB>(y<SUB>0</SUB>)
(4.1)</SPAN></P>
<P>其中：X0，Y0为输入。</P>
<P>则从控制规则中得到的控制为：</P>
<P><SPAN
style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">μ</SPAN><SUB>c</SUB>(z)＝V<SUB>i</SUB>[<SPAN
style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">α</SPAN><SUB>i</SUB></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">μ</SPAN><SUB>ci</SUB>(z)]
(4.2)</P>
<P>对于Takagi-Sugeno推理，控制规则的形式为：</P>
<P>Ri：if x is Ai and y is Bi then Z=fi(x,y)每条规则的击发强度为</P>
<P><SPAN
style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">α</SPAN><SUB>i</SUB>=μ<SUB>Ai</SUB>(X<SUB>0</SUB>)Λμ<SUB>Bi</SUB>(y<SUB>0</SUB>)</SPAN></P>
<P>则从所有控制规则推得的结果为</P>
<TABLE cellSpacing=0 cellPadding=0 width="80%" align=center border=0>
<TBODY>
<TR>
<TD width="82%"><IMG height=68 src="17.files/7.htm47.gif" width=192
border=0></TD>
<TD width="18%">(4.3)</TD></TR></TBODY></TABLE></TD></TR>
<TR>
<TD width="100%" height=1033>
<P>很明显对于Mamdani推理，采用模糊神经元就可以建立模糊控制器；对于Takagi-Sugeno推理，则需要常规神经元和模糊神经元组成的网络来完成。故而．不同的推理方式对应的模糊神经网络有所不同。
</P>
<P align=center><A name="4．1 神经模糊控制器">4．1 神经模糊控制器</A></P>
<P>神经模糊控制器是用神经网络构成的模糊控制器；神经模糊控制器是神经模糊控制的核心。神经模糊控制器最关留的是结构和学习问题。</P>
<P>神经模糊控制器的结构应该是一种这样的拓扑结构，它可以处理模糊信息，并能完成模糊推理。</P>
<P>神经模糊控制器的学习则是一种能完成模糊推理的神经网络的学习。</P>
<P>在这一节中，介绍神经模糊控制器的结构及学习算法。</P>
<P>4．1．1 逻辑神经元组成的神经模糊控制器</P>
<P>逻辑神经元是模糊神经元的一种类型，用逻辑神经元可以构成执行Mamdani推理的模糊控制器。在这种模糊控制器中，每条控制规则可以用一个模糊神经网络实现。</P>
<P>一、模糊控制系统的参数</P>
<P>考虑一个模糊控制的过程，并且具有如下约定的参数：</P>
<P>在时间t时的输人为u(t)，输出为y(t)；设给定为s，则S也是输出的目标值。</P>
<P>设采样周期为T，并在离散时间t＝T，2T……时对输出进行检测。则偏差及偏差变化率求取如下：</P>
<P>e(t)=y(t)-s
(4.4)</P>
<P><SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">Δ</SPAN>e(t)=[e(t)-e(t-T)]/T
(4.5)</P>
<P>对于模物控制器，其输入为e(t)，Δe(t)，模糊值输出为O(t)，反模糊化后的输出为U(t)。</P>
<P>模糊控制器的控制规则集为：</P>
<P>R<SUB>r</SUB>：if e=A<SUB>i</SUB> and Δe=B<SUB>i</SUB> then
O=C<SUB>p</SUB></P>
<P>1<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>r<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>g</P>
<P>在神经模糊控制器中，关键的是如何根据输入e、Δe而得到0，也即是实现模糊控制规则。</P>
<P>设A<SUB>i</SUB><SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">∈</SPAN>[a<SUB>1</SUB>，b<SUB>1</SUB>]，B<SUB>j</SUB><SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">∈</SPAN>[a<SUB>2</SUB>，b<SUB>2</SUB>]，C<SUB>p</SUB><SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">∈</SPAN>[a<SUB>3</SUB>，b<SUB>3</SUB>]，则在e、Δe和O的论域中，选取如下离散的点：</P>
<P>1．在[a1，b1]中取的离散点为X<SUB>i</SUB>，并且有：</P>
<P>X<SUB>o</SUB>=a<SUB>1</SUB>
(4.6)</P>
<P>X<SUB>i</SUB>=a<SUB>1</SUB>+i(b<SUB>1</SUB>-a<SUB>1</SUB>)/N<SUB>1</SUB>
(4.7)</P>
<P>其中：1<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>i<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>N<SUB>1</SUB>，N<SUB>1</SUB>为正整数。</P>
<P>2.在[a<SUB>2</SUB>，b<SUB>2</SUB>]中取的离散点为y<SUB>i</SUB>，并且有</P>
<P>y<SUB>o</SUB>=a<SUB>2</SUB>
(4.8)</P>
<P>y<SUB>i</SUB>=a<SUB>2</SUB>+i(b<SUB>2</SUB>-a<SUB>2</SUB>)/N<SUB>2</SUB>
(4.9)</P>
<P>其中：1<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>i<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>N<SUB>2</SUB>，N<SUB>2</SUB>为正整数。</P>
<P>3．在[a<SUB>3</SUB>,b<SUB>3</SUB>]中取的离散点为Z<SUB>i</SUB>，并且有</P>
<P>Z<SUB>o</SUB>=a<SUB>3</SUB>
(4.10)</P>
<P>Z<SUB>i</SUB>=a<SUB>3</SUB>+i(b<SUB>3</SUB>-a<SUB>3</SUB>)/N<SUB>3 </SUB>
(4.11)</P>
<P>其中：1<i<N<SUB>3</SUB>，N<SUB>3</SUB>为正整数。</P>
<P>对于给出的模糊控制规则中的模糊量A<SUB>i</SUB>，B<SUB>j</SUB>，C<SUB>p</SUB>则有离散的隶属度：</P>
<P>A<SUB>i</SUB>(x<SUB>j</SUB>),0<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>j<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>N<SUB>1</SUB></P>
<P>B<SUB>j</SUB>(y<SUB>k</SUB>),0<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>k<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>N<SUB>2</SUB></P>
<P>C<SUB>p</SUB>(Z<SUB>i</SUB>),0<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>i<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>N<SUB>3</SUB></P>
<P>二、实现控制规则的神经网络</P>
<P>逻辑神经元组成的模糊神经网络如图4—1中所示。它有m个输入神经元，分别表示为I<SUB>1</SUB>，I<SUB>2</SUB>……I<SUB>m</SUB>；同时有n个输出神经元，分别表示为Q<SUB>1</SUB>，Q<SUB>2</SUB>，…，Q<SUB>n</SUB>。</P>
<P>设训练数据集为输入V<SUB>k</SUB>和目标D<SUB>k</SUB>，1<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>k<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>K，并且V<SUB>k</SUB>和D<SUB>k</SUB>都是向量：</P>
<P>V<SUB>k</SUB>=(V<SUB>k1</SUB>,V<SUB>k2</SUB>,……,V<SUB>km</SUB>)
(4.12)</P>
<P>D<SUB>k</SUB>=(D<SUB>k1</SUB>,D<SUB>k2</SUB>,……,D<SUB>kn</SUB>)
(4.13)</P>
<P>在给定输入为V<SUB>k</SUB>时，有输出向量Q<SUB>k</SUB>：</P>
<P>Q<SUB>k</SUB>=(Q<SUB>k1</SUB>,Q<SUB>k2</SUB>,……,Q<SUB>kn</SUB>)
(4.14)</P>
<P>在输入神经元I<SUB>j</SUB>和输出神经元Q<SUB>i</SUB>之间的权系数为r<SUB>ji</SUB>，i＝1，2，……，n，
j＝1，2，……，m。</P>
<P>在输出神经元Q<SUB>i</SUB>中有偏置项<SPAN
⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -