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<P align=center>图4-13 模糊控制系统</P></TD></TR>
<TR>
<TD width="100%" height=69>
<P>在给出了SFIN的初始化参数之后，则可以对SFIN进行在线自适应学习优化。在优化时采用如下性能指标： </P>
<TABLE cellSpacing=0 cellPadding=0 width="80%" align=center border=0>
<TBODY>
<TR>
<TD width="85%"><IMG height=45 src="18.files/7.2.ht13.gif" width=541
border=0></TD>
<TD width="15%">(4.62)</TD></TR>
<TR>
<TD width="85%"><FONT
size=2>其中：h是偏差平方累加个数，<BR>l是加权控制增量平方累加个数，<BR><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>(i)是加权因子。<BR>在上式中y<SUB>d</SUB>(k-i)-y(k-i)＝e(k-i)，即偏差。<BR>在线自适应时系统SFIN中参数W的校正采用下式</FONT></TD>
<TD width="15%"></TD></TR>
<TR>
<TD width="85%"><IMG height=41 src="18.files/7.2.ht14.gif" width=321
border=0></TD>
<TD width="15%">(4.63)</TD></TR></TBODY></TABLE></TD></TR>
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<TD width="100%" height=98>
<P>在式(4．63)中，对J(k)的偏微分求取如下 </P>
<P><IMG height=128 src="18.files/7.2.ht20.gif" width=620 border=0></P>
<P>很明显<SUP>a</SUP>J(k)/<SUP>a</SUP>w和<SUP>a</SUP><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>u(k-i-1)/<SUP>a</SUP>w成比例．即有</P>
<TABLE cellSpacing=0 cellPadding=0 width="80%" align=center border=0>
<TBODY>
<TR>
<TD width="86%"><IMG height=51 src="18.files/7.2.ht21.gif" width=576
border=0></TD>
<TD width="14%">(4.65)</TD></TR>
<TR>
<TD width="86%"><FONT size=2>在上面式子中，<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>u(k-i)是可从神经网络的输出求得的</FONT></TD>
<TD width="14%"></TD></TR>
<TR>
<TD width="86%"><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>u(k-i)=SFIN[e(k-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">Δ</SPAN>e(k-i);W(k)]</TD>
<TD width="14%">(4.66)</TD></TR></TBODY></TABLE></TD></TR>
<TR>
<TD width="100%" height=20>
<P>3．控制系统的运行结果 </P>
<P>对于给定的对象，采用SFIN可实现神经模糊控制并取满意的结果。</P>
<P>(1)被控对象PL</P>
<P>被控对象PL表示如下：</P>
<P>PL(V<SUB>1</SUB>,V<SUB>2</SUB>,V<SUB>3</SUB>,V<SUB>4</SUB>,V<SUB>5</SUB>,y<SUB>d</SUB>)</P>
<P>其中：y<SUB>d</SUB>是设定的期望点。</P>
<P>被控对象的输入输出关系由下式表示</P>
<P>y<SUB>k+1</SUB>=f(y<SUB>k</SUB>,y<SUB>k-1</SUB>,y<SUB>k-2</SUB>)+g(k,y<SUB>k-3</SUB>,y<SUB>k-4</SUB>,U<SUB>k-2</SUB>)+(1.1+V<SUB>1</SUB>)u<SUB>k-1</SUB>+(1+V<SUB>2</SUB>)u<SUB>k</SUB>+Z<SUB>k</SUB>
(4.67)</P>
<P>其中：</P>
<DIV align=center>
<CENTER>
<TABLE cellSpacing=0 cellPadding=0 width="80%" border=0>
<TBODY>
<TR>
<TD width="76%"><IMG height=56 src="18.files/7.2.ht22.gif" width=358
border=0></TD>
<TD width="24%">(4.68)</TD></TR></TBODY></TABLE></CENTER></DIV></TD></TR>
<TR>
<TD width="100%" height=241>
<P>g(k,y<SUB>k-3</SUB>,y<SUB>k-4</SUB>,U<SUB>k-2</SUB>)=V<SUB>4</SUB>Sin[0.08(y<SUB>k-3</SUB>+y<SUB>k-4</SUB>)]U<SUB>k-2</SUB>+V<SUB>5</SUB>cos(0.05k<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">π</SPAN>)
(4.69) </P>
<P>g(·)是干扰信号，</P>
<P>V<SUB>i</SUB>(i＝1，2，…，5)是实参数。</P>
<P>Z<SUB>k</SUB>是白噪声，其最大幅值为0．1。</P>
<P>(2)训练数据集</P>
<P>给出的训练数据集如表4—1所示，它一共有30组训练数据。这些数据用于对SFIN进行初始化监视学习，从而确定SFIN的初始参数。</P>
<P align=center>表4-1 数据训练集</P>
<DIV align=center>
<CENTER>
<TABLE cellSpacing=1 cellPadding=0 width="80%" bgColor=#808080 border=0>
<TBODY>
<TR>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>k</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>E(k)</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT size=2><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">Δ</SPAN>E(k)</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT size=2><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">Δ</SPAN>U(k)</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>k</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>E(k)</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT size=2><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">Δ</SPAN>E(k)</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT size=2><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">Δ</SPAN>U(k)</FONT></TD></TR>
<TR>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>1</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>3.0000</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>0.0000</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>0.1893</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>16</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>-0.1472</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>-0.5316</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>0.0462</FONT></TD></TR>
<TR>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>2</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>2.8228</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>-0.1772</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>0.1732</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>17</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>-0.2259</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>-0.0787</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>0.0024</FONT></TD></TR>
<TR>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>3</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>2.3440</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>-0.4788</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>0.1421</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>18</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>-0.1874</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>0.0385</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>-0.0040</FONT></TD></TR>
<TR>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>4</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>1.6426</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>-0.7014</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>0.1063</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>19</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>0.0424</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>0.2298</FONT></TD>
<TD align=middle width="13%" bgColor=#ffffff><FONT
size=2>0.0079</FONT></TD></TR>
<TR>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>5</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
size=2>0.5628</FONT></TD>
<TD align=middle width="12%" bgColor=#ffffff><FONT
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