* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
-->
-<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" version="5.0-subset Scilab" xml:lang="en" xml:id="inistate">
- <info>
- <pubdate>$LastChangedDate$</pubdate>
- </info>
- <refnamediv>
- <refname>inistate</refname>
- <refpurpose> Estimates the initial state of a discrete-time system</refpurpose>
- </refnamediv>
- <refsynopsisdiv>
- <title>Calling Sequence</title>
- <synopsis>X0 = inistate(SYS,Y,U,TOL,PRINTW)
-X0 = inistate(A,B,C,Y,U);
-X0 = inistate(A,C,Y);
-
-[x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW)</synopsis>
- </refsynopsisdiv>
- <refsection>
- <title>Arguments</title>
- <variablelist>
- <varlistentry>
- <term>SYS</term>
- <listitem>
- <para>given system, syslin(dt,A,B,C,D)</para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>Y</term>
- <listitem>
- <para>the output of the system</para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>U</term>
- <listitem>
- <para>the input of the system</para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>TOL</term>
- <listitem>
- <para>TOL is the tolerance used for estimating the rank of matrices. If TOL > 0, then the given value of TOL is used as a lower bound for the reciprocal condition number.</para>
- <para>
- Default: prod(size(matrix))*epsilon_machine where epsilon_machine is the relative machine precision.
- </para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>PRINTW</term>
- <listitem>
- <para>PRINTW is a switch for printing the warning messages.</para>
- <variablelist>
+<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="en" xml:id="inistate">
+ <refnamediv>
+ <refname>inistate</refname>
+ <refpurpose>Estimates the initial state of a discrete-time system</refpurpose>
+ </refnamediv>
+ <refsynopsisdiv>
+ <title>Calling Sequence</title>
+ <synopsis>X0 = inistate(SYS,Y,U,TOL,PRINTW)
+ X0 = inistate(A,B,C,Y,U);
+ X0 = inistate(A,C,Y);
+
+ [x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW)
+ </synopsis>
+ </refsynopsisdiv>
+ <refsection>
+ <title>Arguments</title>
+ <variablelist>
+ <varlistentry>
+ <term>SYS</term>
+ <listitem>
+ <para>given system, syslin(dt,A,B,C,D)</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Y</term>
+ <listitem>
+ <para>the output of the system</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>U</term>
+ <listitem>
+ <para>the input of the system</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>TOL</term>
+ <listitem>
+ <para>TOL is the tolerance used for estimating the rank of matrices. If TOL > 0, then the given value of TOL is used as a lower bound for the reciprocal condition number.</para>
+ <para>
+ Default: prod(size(matrix))*epsilon_machine where epsilon_machine is the relative machine precision.
+ </para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>PRINTW</term>
+ <listitem>
+ <para>PRINTW is a switch for printing the warning messages.</para>
+ <variablelist>
+ <varlistentry>
+ <term>= </term>
+ <listitem>
+ <para>1: print warning messages;</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>= </term>
+ <listitem>
+ <para>0: do not print warning messages.</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ <para>
+ Default: PRINTW = 0.
+ </para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>X0</term>
+ <listitem>
+ <para>the estimated initial state vector</para>
+ </listitem>
+ </varlistentry>
<varlistentry>
- <term>= </term>
- <listitem>
- <para>1: print warning messages;</para>
- </listitem>
+ <term>V</term>
+ <listitem>
+ <para>orthogonal matrix which reduces the system state matrix A to a real Schur form</para>
+ </listitem>
</varlistentry>
<varlistentry>
- <term>= </term>
- <listitem>
- <para>0: do not print warning messages.</para>
- </listitem>
+ <term>rcnd</term>
+ <listitem>
+ <para>estimate of the reciprocal condition number of the coefficient matrix of the least squares problem solved.</para>
+ </listitem>
</varlistentry>
- </variablelist>
- <para>
- Default: PRINTW = 0.
- </para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>X0</term>
- <listitem>
- <para>the estimated initial state vector</para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>V</term>
- <listitem>
- <para>orthogonal matrix which reduces the system state matrix A to a real Schur form</para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>rcnd</term>
- <listitem>
- <para>estimate of the reciprocal condition number of the coefficient matrix of the least squares problem solved.</para>
- </listitem>
- </varlistentry>
- </variablelist>
- </refsection>
- <refsection>
- <title>Description</title>
- <para>
- inistate Estimates the initial state of a discrete-time system, given the
- (estimated) system matrices, and a set of input/output data.</para>
- <para>
- X0 = inistate(SYS,Y,U,TOL,PRINTW) estimates the initial state X0 of
- the discrete-time system SYS = (A,B,C,D), using the output data Y
- and the input data U. The model structure is :</para>
- <programlisting role = ""><![CDATA[
+ </variablelist>
+ </refsection>
+ <refsection>
+ <title>Description</title>
+ <para>
+ inistate Estimates the initial state of a discrete-time system, given the
+ (estimated) system matrices, and a set of input/output data.
+ </para>
+ <para>
+ X0 = inistate(SYS,Y,U,TOL,PRINTW) estimates the initial state X0 of
+ the discrete-time system SYS = (A,B,C,D), using the output data Y
+ and the input data U. The model structure is :
+ </para>
+ <programlisting role=""><![CDATA[
x(k+1) = Ax(k) + Bu(k), k >= 1,
y(k) = Cx(k) + Du(k),
]]></programlisting>
- <para>
- The vectors y(k) and u(k) are transposes of the k-th rows of Y and U,
- respectively.</para>
- <para>
- Instead of the first input parameter SYS (an syslin object), equivalent
- information may be specified using matrix parameters, for instance,
- X0 = inistate(A,B,C,Y,U); or X0 = inistate(A,C,Y);</para>
- <para>
- [x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW) returns, besides x0,
- the orthogonal matrix V which reduces the system state matrix A to
- a real Schur form, as well as an estimate of the reciprocal condition
- number of the coefficient matrix of the least squares problem solved.</para>
- </refsection>
- <refsection role="see also">
-<title>See Also</title>
- <simplelist type="inline">
- <member>
- <link linkend="findBD">findBD</link>
- </member>
- <member>
- <link linkend="findx0BD">findx0BD</link>
- </member>
- </simplelist>
- </refsection>
+ <para>
+ The vectors y(k) and u(k) are transposes of the k-th rows of Y and U,
+ respectively.
+ </para>
+ <para>
+ Instead of the first input parameter SYS (an syslin object), equivalent
+ information may be specified using matrix parameters, for instance,
+ X0 = inistate(A,B,C,Y,U); or X0 = inistate(A,C,Y);
+ </para>
+ <para>
+ [x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW) returns, besides x0,
+ the orthogonal matrix V which reduces the system state matrix A to
+ a real Schur form, as well as an estimate of the reciprocal condition
+ number of the coefficient matrix of the least squares problem solved.
+ </para>
+ </refsection>
+ <refsection>
+ <title>Examples</title>
+ <programlisting role="example"><![CDATA[
+//generate data from a given linear system
+A = [ 0.5, 0.1,-0.1, 0.2;
+ 0.1, 0, -0.1,-0.1;
+ -0.4,-0.6,-0.7,-0.1;
+ 0.8, 0, -0.6,-0.6];
+B = [0.8;0.1;1;-1];
+C = [1 2 -1 0];
+SYS=syslin(0.1,A,B,C);
+nsmp=100;
+U=prbs_a(nsmp,nsmp/5);
+Y=(flts(U,SYS)+0.3*rand(1,nsmp,'normal'));
+
+// Compute R
+S=15;
+[R,N1,SVAL] = findR(S,Y',U');
+N=3;
+SYS1 = findABCD(S,N,1,R) ;
+SYS1.dt=0.1;
+
+inistate(SYS1,Y',U')
+
+]]></programlisting>
+ </refsection>
+ <refsection role="see also">
+ <title>See Also</title>
+ <simplelist type="inline">
+ <member>
+ <link linkend="findBD">findBD</link>
+ </member>
+ <member>
+ <link linkend="findx0BD">findx0BD</link>
+ </member>
+ </simplelist>
+ </refsection>
</refentry>
projects / scilab.git / blobdiff