📄 17.htm
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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">θ</SPAN><SUB>i</SUB>，用<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">θ</SPAN>表示<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">θ</SPAN><SUB>i</SUB>向量，则有：</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">θ=(θ<SUB>1</SUB>,θ<SUB>2</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">θ<SUB>n</SUB>)
(4.15)</SPAN></P>
<P align=center><IMG height=259 src="17.files/7.htm48.gif" width=603
border=0></P>
<P align=center>图4-1 模糊神经网络</P></TD></TR>
<TR>
<TD width="100%" height=18>
<P>在图4—1中，神经元是逻辑神经元，故而当给定输入V<SUB>k</SUB>后，则有输出 </P>
<P align=center><IMG height=224 src="17.files/7.htm49.gif" width=506
border=0></P>
<P>也可以用一个通式表示上面所有的n个式子</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">Q<SUB>ki</SUB>=[(V<SUB>k1</SUB>∧r<SUB>li</SUB>)∨......∨(V<SUB>km</SUB>∧r<SUB>mi</SUB>)]∨θ<SUB>i</SUB>
(4.16)</SPAN></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">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</SPAN></P>
<P>在图4—1中，把输入V<SUB>k</SUB>看成是一个行向量，把偏置项<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">θ</SPAN>看成—个行向量，并令</P>
<TABLE cellSpacing=0 cellPadding=0 width="80%" align=center border=0>
<TBODY>
<TR>
<TD width="77%"><IMG height=89 src="17.files/7.htm50.gif" width=243
border=0></TD>
<TD width="23%">(4.17)</TD></TR></TBODY></TABLE></TD></TR>
<TR>
<TD width="100%" height=669>
<P>则可以用向量方程描述神经网络的输入和输出如下 </P>
<P>Q<SUB>k</SUB>=(V<SUB>k</SUB>oR)<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">∨θ</SPAN>
(4.18)</P>
<P>对于模糊控制器而言，它可以是由控制规则集组成。对于控制规则集</P>
<P>R<SUB>r</SUB>:if e=Ai and <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=Bj
then Q=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>则可以用一个神经网络模块实现一条规则，如果用n个神经网络模块则可以实现n条规则；也即是实现一个模糊控制器。</P>
<P>下面说明如何用一个神经网络模块实现一条控制规则。</P>
<P>在图4—1所示的神经网络可看成一个模块。根据式(4．6)(4．7)所表示的模糊量Ai所取的离散点有N<SUB>1</SUB>+1个；式(4．8)(4．9)所表示的模糊量Bj所取的离散点有N<SUB>2</SUB>+1个；式(4．10)(4．11)所表示的模糊量C<SUB>p</SUB>所取的离散点有N<SUB>3</SUB>+1个。令图4—1所示的神经网络模块中。</P>
<P>m=(N<SUB>1</SUB>+1)+(N<SUB>2</SUB>+1)=N<SUB>1</SUB>+N<SUB>2</SUB>+2
(4.19)</P>
<P>n=N<SUB>3</SUB>+1
(4.20)</P>
<P>在输人的m个神经元中，把其中的N<SUB>1</SUB>+1个神经元用于输入Ai；其中的N<SUB>2</SUB>+1个神经元用于输入Bj。而输出的n个神经元用于目标C<SUB>p</SUB>。并以此进行学习，则可以在学习结束时，得到能实现一条规则的一个神经网络模块。学习时，</P>
<P>A<SUB>i</SUB>(X<SUB>0</SUB>)——I<SUB>1</SUB></P>
<P>A<SUB>i</SUB>(X<SUB>1</SUB>)——I<SUB>2</SUB></P>
<P>……</P>
<P>A<SUB>i</SUB>(X<SUB>N1</SUB>)——I<SUB>N1</SUB>+1</P>
<P>而同时</P>
<P>B<SUB>j</SUB>(y<SUB>0</SUB>)=I<SUB>N1</SUB>+2</P>
<P>B<SUB>j</SUB>(y<SUB>1</SUB>)=I<SUB>N1</SUB>+3</P>
<P>……</P>
<P>B<SUB>j</SUB>(y<SUB>N2</SUB>)=I<SUB>m</SUB></P>
<P>并且，输出目标为：</P>
<P>C<SUB>p</SUB>(Z<SUB>0</SUB>)——Q<SUB>1</SUB></P>
<P>C<SUB>p</SUB>(Z<SUB>1</SUB>)——Q<SUB>2</SUB></P>
<P>……</P>
<P>C<SUB>p</SUB>(Z<SUB>N3</SUB>)——Q<SUB>n</SUB></P>
<P>在控制规则集中，一共有g条规则，最后用g个神经网络模块，则可以实现模糊控制器。这个控制器即是神经模糊控制器。</P>
<P>4．1．2 神经模糊控制器的学习算法</P>
<P>图4—1所示的逻辑神经网络所组成的神经模糊控制器可以用改进的梯度法进行学习。</P>
<P>设给出的训练输人为Vk，目标为Dk，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：</P>
<P>V<SUB>k</SUB>=(V<SUB>k1</SUB>,V<SUB>k2</SUB>,…,V<SUB>km</SUB>)</P>
<P>D<SUB>k</SUB>=(D<SUB>k1</SUB>,D<SUB>k2</SUB>,…,D<SUB>kn</SUB>)</P>
<P>而图4—1所示的网络在输入为V<SUB>k</SUB>时，实际输出为Q<SUB>k</SUB>。学习的目的，则是令Q<SUB>k</SUB>逼近于D<SUB>k</SUB>。实质上，就是修改网络的权系数r<SUB>ji</SUB>，使到网络的插出Q<SUB>k</SUB>趋于目标D<SUB>k</SUB>。换而言之，也即是使式(4．18)中的Q<SUB>k</SUB>＝D<SUB>k</SUB>时，求其解R。即在</P>
<P>D<SUB>k</SUB>=(V<SUB>k</SUB>oR)<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">∨θ </SPAN>
(4.21)</P>
<P>中，给出Dk，Vk，<SPAN
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<P>为了进行学习，取目标函数J</P>
<TABLE cellSpacing=0 cellPadding=0 width="80%" align=center border=0>
<TBODY>
<TR>
<TD width="74%"><IMG height=44 src="17.files/7.htm51.gif" width=202
border=0></TD>
<TD width="26%">(4.22)</TD></TR>
<TR>
<TD width="74%"><FONT size=2>学习算法是采用改进的梯度算法，这个算法用下面两个公式表示</FONT></TD>
<TD width="26%"></TD></TR>
<TR>
<TD width="74%"><IMG height=26 src="17.files/7.htm52.gif" width=381
border=0></TD>
<TD width="26%">(4.23)</TD></TR>
<TR>
<TD width="74%"><IMG height=24 src="17.files/7.htm53.gif" width=373
border=0></TD>
<TD width="26%">(4.24)</TD></TR></TBODY></TABLE></TD></TR>
<TR>
<TD width="100%" height=18>
<P>其中：l＝1，2，3，……是迭代次数 </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">η</SPAN><SUB>i</SUB>，i＝1，2，是学习速率，</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">α</SPAN><SUB>i</SUB>，i＝1，2，是动量常数。</P>
<P>在式(4．23)(4．24)中，<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>r<SUB>ji</SUB>和<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><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">θ</SPAN><SUB>i</SUB>的意义如下</P>
<TABLE cellSpacing=0 cellPadding=0 width="80%" align=center border=0>
<TBODY>
<TR>
<TD width="74%"><IMG height=47 src="17.files/7.htm54.gif" width=87
border=0></TD>
<TD width="26%">(4.25)</TD></TR>
<TR>
<TD width="74%"><IMG height=44 src="17.files/7.htm55.gif" width=86
border=0></TD>
<TD width="26%">(4.26)</TD></TR>
<TR>
<TD width="74%"><FONT size=2>对于<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>r<SUB>ji</SUB>，可计算如下</FONT></TD>
<TD width="26%"></TD></TR>
<TR>
<TD width="74%"><IMG height=50 src="17.files/7.htm56.gif" width=224
border=0></TD>
<TD width="26%">(4.27)</TD></TR>
<TR>
<TD width="74%"><IMG height=58 src="17.files/7.htm57.gif" width=202
border=0></TD>
<TD width="26%">(4.28)</TD></TR></TBODY></TABLE></TD></TR>
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