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[scilab.git] / scilab / modules / cacsd / help / ja_JP / leqr.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2 <!--
3  * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
4  * Copyright (C) INRIA - F. Delebecque
5  * 
6  * Copyright (C) 2012 - 2016 - Scilab Enterprises
7  *
8  * This file is hereby licensed under the terms of the GNU GPL v2.0,
9  * pursuant to article 5.3.4 of the CeCILL v.2.1.
10  * This file was originally licensed under the terms of the CeCILL v2.1,
11  * and continues to be available under such terms.
12  * For more information, see the COPYING file which you should have received
13  * along with this program.
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15  -->
16 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="ja" xml:id="leqr">
17     <refnamediv>
18         <refname>leqr</refname>
19         <refpurpose>H無限大 LQ ゲイン (全状態)  </refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>呼び出し手順</title>
23         <synopsis>[K,X,err]=leqr(P12,Vx)</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>パラメータ</title>
27         <variablelist>
28             <varlistentry>
29                 <term>P12</term>
30                 <listitem>
31                     <para>
32                         <literal>syslin</literal> リスト
33                     </para>
34                 </listitem>
35             </varlistentry>
36             <varlistentry>
37                 <term>Vx</term>
38                 <listitem>
39                     <para>対称非負定行列 (十分に小さい必要があります)</para>
40                 </listitem>
41             </varlistentry>
42             <varlistentry>
43                 <term>K,X</term>
44                 <listitem>
45                     <para>実数行列</para>
46                 </listitem>
47             </varlistentry>
48             <varlistentry>
49                 <term>err</term>
50                 <listitem>
51                     <para>実数 (リカッチ方程式の左辺のl1ノルム)</para>
52                 </listitem>
53             </varlistentry>
54         </variablelist>
55     </refsection>
56     <refsection>
57         <title>説明</title>
58         <para>
59             <literal>leqr</literal>  は,
60             連続または離散時間系のプラント <literal>P12=[A,B2,C1,D12]</literal>に関して
61             線形準最適H無限大LQ全状態ゲインを計算します.
62         </para>
63         <para>
64             <literal>P12</literal> は <literal>syslin</literal> リストです (例: <literal>P12=syslin('c',A,B2,C1,D12)</literal>).
65         </para>
66         <programlisting role=""><![CDATA[ 
67 [C1' ]               [Q  S]
68 [    ]  * [C1 D12] = [    ]
69 [D12']               [S' R]
70  ]]></programlisting>
71         <para>
72             <literal>Vx</literal> は,
73             <literal>x</literal>の外乱の
74             ノイズ <literal>w</literal> の共分散行列に関連します
75             (通常, <literal>Vx=gama^-2*B1*B1'</literal>).
76         </para>
77         <para>
78             ゲイン <literal>K</literal> は, <literal>A + B2*K</literal> が安定となるように設定されます.
79         </para>
80         <para>
81             <literal>X</literal> はリカッチ方程式の安定解です.
82         </para>
83         <para>
84             連続プラントの場合:
85         </para>
86         <programlisting role=""><![CDATA[ 
87 (A-B2*inv(R)*S')'*X+X*(A-B2*inv(R)*S')-X*(B2*inv(R)*B2'-Vx)*X+Q-S*inv(R)*S'=0
88  ]]></programlisting>
89         <programlisting role=""><![CDATA[ 
90 K=-inv(R)*(B2'*X+S)
91  ]]></programlisting>
92         <para>
93             離散時間プラントの場合:
94         </para>
95         <programlisting role=""><![CDATA[ 
96 X-(Abar'*inv((inv(X)+B2*inv(R)*B2'-Vx))*Abar+Qbar=0
97  ]]></programlisting>
98         <programlisting role=""><![CDATA[ 
99 K=-inv(R)*(B2'*inv(inv(X)+B2*inv(R)*B2'-Vx)*Abar+S')
100  ]]></programlisting>
101         <para>
102             ただし, <literal>Abar=A-B2*inv(R)*S'</literal> および <literal>Qbar=Q-S*inv(R)*S'</literal>
103         </para>
104         <para>
105             これらのリカッチ方程式に関連する3ブロック行列ペンシルは次のように
106             なります:
107         </para>
108         <programlisting role=""><![CDATA[ 
109              離散系                        連続系
110  |I  -Vx  0|   | A    0    B2|       |I   0   0|   | A    Vx    B2|
111 z|0   A'  0| - |-Q    I    -S|      s|0   I   0| - |-Q   -A'   -S |
112  |0   B2' 0|   | S'   0     R|       |0   0   0|   | S'   -B2'   R|
113  ]]></programlisting>
114     </refsection>
115     <refsection role="see also">
116         <title>参照</title>
117         <simplelist type="inline">
118             <member>
119                 <link linkend="lqr">lqr</link>
120             </member>
121         </simplelist>
122     </refsection>
123 </refentry>