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<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>0.3844</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>-1.1769</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>0.0893</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>30</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>0.2653</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>0.0535</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>0.0207</FONT></TD></TR></TBODY></TABLE></CENTER></DIV></TD></TR>
<TR>
<TD width="100%" height=437>
<P>(3)自适应在线学习及结果 </P>
<P>考虑对有关的参数学习时所选取的值如下：</P>
<P>前件有关参数有偏差e的模糊量参数a<SUB>e</SUB>,b<SUB>e</SUB>,c<SUB>e</SUB>；偏差变化率<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的模糊量参数a<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">Δ</SPAN>e</SUB>,b<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">Δ</SPAN>e</SUB>,c<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">Δ</SPAN>e</SUB>,在学习这些参数时的学习速率<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>分别选值为</P>
<P>a<SUB>e</SUB>,a<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">Δ</SPAN>e</SUB>,c<SUB>e</SUB>,c<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">Δ</SPAN>e</SUB>的学习速率<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>＝10<SUP>-6</SUP></P>
<P>b<SUB>e</SUB>,b<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">Δ</SPAN>e</SUB>学习速率<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>=10<SUP>-8</SUP></P>
<P>后件有关参数是其二项式参数P，它的学习速率<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>＝0．00125。</P>
<P>在学习时所用的式(4．65)中的参数取：</P>
<P>h=1 l=0 <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=15</SPAN></P>
<P>同时，学习公式(4．63)的迭代步数取3。</P>
<P>系统运行的情况如图4—14所示。</P>
<P align=center><IMG height=337 src="18.files/7.2.ht23.gif" width=613
border=0></P>
<P align=center>图4-14 较大干扰时SFIN运行情况</P></TD></TR>
<TR>
<TD width="100%" height=295>
<P>在图4—14中分别给出了3条响应曲线，这3条响应曲线分别用<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">①②③</SPAN>标记。
</P>
<P>对于响应曲线<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">①</SPAN>，它是把设定点在k＝50时进行改变的响应情况。这时被控对象参数变化如下：</P>
<P>PL(0,0,0,0,0,3.5)——PL(0,0,0,0,0,7.0)</P>
<P>对于响应曲线<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">②</SPAN>，它是在k=70时参数改变所产生的响应情况。被控对象参数改变如下：</P>
<P>PL(0,0,0,0,0,6.0)——PL(-0.25,0.45,0.5,0,0,6.0)</P>
<P>对于响应曲线②，它是在k＝30时产生干扰的响应情况。被控对象参数改变如下</P>
<P>PL(0,0,0,0,0,4.5)——PL(0,0,0,0.35,0.25,4.5)</P>
<P>单向线性响应URL(Unidirectional Linear
Response)神经元可以构成模糊神经网络，从而可以构成神经模糊控制器。在这一节中介绍用URL模糊网络控制的控制系统。</P>
<P>1．URL模糊网络</P>
<P>ULR神经元是在输入信号取值为正时有线性特性，而输人为负时则输出为零的神经元。URL神经元的结构和特性可用图4—15说明。在图中，(a)是神经元结构，可见它和一般神经元是一样的；(b)是神经元特性．可见它取正值时为线性，而输入取负值时则输出为零。</P>
<DIV align=center>
<CENTER>
<TABLE cellSpacing=0 cellPadding=0 width="80%" border=0>
<TBODY>
<TR>
<TD align=middle width="50%"><IMG height=157
src="18.files/7.2.ht24.gif" width=222 border=0>
<P align=center>(a)</P></TD>
<TD align=middle width="50%"><IMG height=174
src="18.files/7.2.ht25.gif" width=268 border=0>
<P></P>
<P align=center>(b)</P></TD></TR></TBODY></TABLE></CENTER></DIV></TD></TR>
<TR>
<TD width="100%" height=11>
<P align=center>图4-15 URL神经元及特性</P>
<P>在图4—15中，x<SUB>1</SUB>，x<SUB>2</SUB>，……，x<SUB>n</SUB>是输入的模糊变量，U<SUB>x1</SUB>，U<SUB>x2</SUB>，……，U<SUB>xm</SUB>分别是对应的隶属函数，W<SUB>i</SUB>是x<SUB>i</SUB>，i＝1，2，……，n和神经元的连接权系数，<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>是阀值，f(x)是神经元的输出，则有：</P>
<DIV align=center>
<CENTER>
<TABLE cellSpacing=0 cellPadding=0 width="80%" border=0>
<TBODY>
<TR>
<TD width="77%"><IMG height=42 src="18.files/7.2.ht26.gif" width=130
border=0></TD>
<TD width="23%">(4.70)</TD></TR>
<TR>
<TD width="77%"><IMG height=54 src="18.files/7.2.ht27.gif" width=205
border=0></TD>
<TD width="23%">(4.71)</TD></TR></TBODY></TABLE></CENTER></DIV></TD></TR>
<TR>
<TD width="100%" height=183>
<P>采用URL神经元组成单层或多层神经网络，并可以实现各种基本或组合的模糊逻辑函数。 </P>
<P>例1 用URL网络实现模糊蕴含关系：</P>
<P><IMG height=25 src="18.files/7.2.ht28.gif" width=210 border=0></P>
<P>考虑URL网络的结构如图4—16所示。它一共有3个URL神经元，并分为2层。输人有2个模糊量U<SUB>x</SUB>+U<SUB>y</SUB>。</P>
<P align=center><IMG height=146 src="18.files/7.2.ht29.gif" width=456
border=0></P>
<P align=center>图4-16 URL网络</P></TD></TR>
<TR>
<TD width="100%" height=2>
<P>很明显，作为输出U<SUB>x——y</SUB>=f3，即有 </P>
<DIV align=center>
<CENTER>
<TABLE cellSpacing=0 cellPadding=0 width="80%" border=0>
<TBODY>
<TR>
<TD width="62%"><IMG height=26 src="18.files/7.2.ht30.gif" width=223
border=0></TD>
<TD width="38%">(4.72)</TD></TR></TBODY></TABLE></CENTER></DIV></TD></TR>
<TR>
<TD width="100%" height=674>
<P>令 </P>
<P><IMG height=88 src="18.files/7.2.ht31.gif" width=92 border=0></P>
<P>故有：<IMG height=25 src="18.files/7.2.ht32.gif" width=139 border=0></P>
<P>从图4—16中，可以看出f<SUB>1</SUB>、f<SUB>2</SUB>的求取如下：</P>
<P>f<SUB>1</SUB>=f(W<SUB>1</SUB>'U<SUB>x</SUB>+W<SUB>2</SUB>"U<SUB>y</SUB>-')
<P>f<SUB>2</SUB>=f(W<SUB>1</SUB>"U<SUB>x</SUB>+W<SUB>2</SUB>'U<SUB>y</SUB>-")
<P>令
<P><IMG height=132 src="18.files/7.2.ht33.gif" width=150 border=0>
<P>f<SUB>1</SUB>=f(-U<SUB>x</SUB>+U<SUB>y</SUB>+1)
<P>f<SUB>2</SUB>=f(-U<SUB>x</SUB>+U<SUB>y</SUB>)
<P>显然
<P><IMG height=61 src="18.files/7.2.ht34.gif" width=352 border=0>
<P><IMG height=62 src="18.files/7.2.ht35.gif" width=343 border=0>
<P><IMG height=93 src="18.files/7.2.ht36.gif" width=363 border=0>
<P><IMG height=95 src="18.files/7.2.ht37.gif" width=455
border=0>
(4.73)</P></TD></TR>
<TR>
<TD width="100%" height=642>
<P>从式(4．73)中可知，当f1>0，f2<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>0时有
</P>
<P><IMG height=24 src="18.files/7.2.ht38.gif" width=161 border=0></P>
<P>这时，由于有f2<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>0，即有</P>
<P>-Ux+Uy<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><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">0</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">也即是
1-Ux+Uy≤1</SPAN></P>
<P>故而式(4．73)表明ULR网络实现的功能为</P>
<P><IMG height=27 src="18.files/7.2.ht39.gif" width=213 border=0></P>
<P>例2 用ULR网络实现有界和功能U<SUB>x<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>y</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">Λ</SPAN>(1-U<SUB>x</SUB>+U<SUB>y</SUB>)。<BR>采用图4—16的同一ULR网络，并且令：</P>
<P><IMG height=89 src="18.files/7.2.ht40.gif" width=89 border=0></P>
<P>则有</P>
<P>U<SUB>x<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>y</SUB>=f(W<SUB>1</SUB>f<SUB>1</SUB>-W<SUB>2</SUB>f<SUB>2</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">θ</SPAN>)<BR>
=f(f<SUB>1</SUB>-f<SUB>2</SUB>)</P>
<P><IMG height=95 src="18.files/7.2.ht41.gif" width=233 border=0></P>
<P>则有</P>
<P> f1=f(Ux+Uy)</P>
<P> f2=f(Ux+Uy-1)</P>
<P>显然</P>
<P> f1=Ux+Uy</P>
<P><IMG height=58 src="18.files/7.2.ht42.gif" width=351 border=0></P>
<P><IMG height=55 src="18.files/7.2.ht43.gif" width=327 border=0></P>
<P><IMG height=60 src="18.files/7.2.ht44.gif" width=417
border=0> (4.74)</P></TD></TR>
<TR>
<TD width="100%" height=364>
<P>当f<SUB>2<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: ⌨️ 快捷键说明
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