X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;f=octave_packages%2Fcontrol-2.3.52%2Fcare.m;fp=octave_packages%2Fcontrol-2.3.52%2Fcare.m;h=c72879029c3079b3b648705cc934bd76d803f1f4;hb=c880e8788dfc484bf23ce13fa2787f2c6bca4863;hp=0000000000000000000000000000000000000000;hpb=1705066eceaaea976f010f669ce8e972f3734b05;p=CreaPhase.git

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+## Copyright (C) 2009, 2010   Lukas F. Reichlin
+##
+## This file is part of LTI Syncope.
+##
+## LTI Syncope is free software: you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation, either version 3 of the License, or
+## (at your option) any later version.
+##
+## LTI Syncope is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with LTI Syncope.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{x}, @var{l}, @var{g}] =} care (@var{a}, @var{b}, @var{q}, @var{r})
+## @deftypefnx {Function File} {[@var{x}, @var{l}, @var{g}] =} care (@var{a}, @var{b}, @var{q}, @var{r}, @var{s})
+## @deftypefnx {Function File} {[@var{x}, @var{l}, @var{g}] =} care (@var{a}, @var{b}, @var{q}, @var{r}, @var{[]}, @var{e})
+## @deftypefnx {Function File} {[@var{x}, @var{l}, @var{g}] =} care (@var{a}, @var{b}, @var{q}, @var{r}, @var{s}, @var{e})
+## Solve continuous-time algebraic Riccati equation (ARE).
+##
+## @strong{Inputs}
+## @table @var
+## @item a
+## Real matrix (n-by-n).
+## @item b
+## Real matrix (n-by-m).
+## @item q
+## Real matrix (n-by-n).
+## @item r
+## Real matrix (m-by-m).
+## @item s
+## Optional real matrix (n-by-m).  If @var{s} is not specified, a zero matrix is assumed.
+## @item e
+## Optional descriptor matrix (n-by-n).  If @var{e} is not specified, an identity matrix is assumed.
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item x
+## Unique stabilizing solution of the continuous-time Riccati equation (n-by-n).
+## @item l
+## Closed-loop poles (n-by-1).
+## @item g
+## Corresponding gain matrix (m-by-n).
+## @end table
+##
+## @strong{Equations}
+## @example
+## @group
+##                -1
+## A'X + XA - XB R  B'X + Q = 0
+## 
+##                      -1
+## A'X + XA - (XB + S) R  (B'X + S') + Q = 0
+##
+##      -1
+## G = R  B'X
+##
+##      -1
+## G = R  (B'X + S')
+##
+## L = eig (A - B*G)
+## @end group
+## @end example
+## @example
+## @group
+##                     -1
+## A'XE + E'XA - E'XB R   B'XE + Q = 0
+##
+##                           -1
+## A'XE + E'XA - (E'XB + S) R   (B'XE + S') + Q = 0
+##
+##      -1
+## G = R  B'XE
+##
+##      -1
+## G = R  (B'XE + S)
+##
+## L = eig (A - B*G, E)
+## @end group
+## @end example
+##
+## @strong{Algorithm}@*
+## Uses SLICOT SB02OD and SG02AD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+##
+## @seealso{dare, lqr, dlqr, kalman}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: November 2009
+## Version: 0.5.1
+
+function [x, l, g] = care (a, b, q, r, s = [], e = [])
+
+  ## TODO: extract feedback matrix g from SB02OD (and SG02AD)
+
+  if (nargin < 4 || nargin > 6)
+    print_usage ();
+  endif
+
+  if (! is_real_square_matrix (a, q, r))
+    ## error ("care: a, q, r must be real and square");
+    error ("care: %s, %s, %s must be real and square", \
+            inputname (1), inputname (3), inputname (4));
+  endif
+  
+  if (! is_real_matrix (b) || rows (a) != rows (b))
+    ## error ("care: a and b must have the same number of rows");
+    error ("care: %s and %s must have the same number of rows", \
+            inputname (1), inputname (2));
+  endif
+  
+  if (columns (r) != columns (b))
+    ## error ("care: b and r must have the same number of columns");
+    error ("care: %s and %s must have the same number of columns", \
+            inputname (2), inputname (4));
+  endif
+
+  if (! is_real_matrix (s) && ! size_equal (s, b))
+    ## error ("care: s(%dx%d) must be real and identically dimensioned with b(%dx%d)",
+    ##         rows (s), columns (s), rows (b), columns (b));
+    error ("care: %s(%dx%d) must be real and identically dimensioned with %s(%dx%d)", \
+            inputname (5), rows (s), columns (s), inputname (2), rows (b), columns (b));
+  endif
+
+  if (! isempty (e) && (! is_real_square_matrix (e) || ! size_equal (e, a)))
+    ## error ("care: a and e must have the same number of rows");
+    error ("care: %s and %s must have the same number of rows", \
+            inputname (1), inputname (6));
+  endif
+
+  ## check stabilizability
+  if (! isstabilizable (a, b, e, [], 0))
+    ## error ("care: (a, b) not stabilizable");
+    error ("care: (%s, %s) not stabilizable", \
+            inputname (1), inputname (2));
+  endif
+
+  ## check positive semi-definiteness
+  if (isempty (s))
+    t = zeros (size (b));
+  else
+    t = s;
+  endif
+
+  m = [q, t; t.', r];
+
+  if (isdefinite (m) < 0)
+    ## error ("care: require [q, s; s.', r] >= 0");
+    error ("care: require [%s, %s; %s.', %s] >= 0", \
+            inputname (3), inputname (5), inputname (5), inputname (4));
+  endif
+
+  ## solve the riccati equation
+  if (isempty (e))
+    if (isempty (s))
+      [x, l] = slsb02od (a, b, q, r, b, false, false);
+      g = r \ (b.'*x);          # gain matrix
+    else
+      [x, l] = slsb02od (a, b, q, r, s, false, true);
+      g = r \ (b.'*x + s.');    # gain matrix
+    endif
+  else
+    if (isempty (s))
+      [x, l] = slsg02ad (a, e, b, q, r, b, false, false);
+      g = r \ (b.'*x*e);        # gain matrix
+    else
+      [x, l] = slsg02ad (a, e, b, q, r, s, false, true);
+      g = r \ (b.'*x*e + s.');  # gain matrix
+    endif
+  endif
+
+endfunction
+
+
+%!shared x, l, g, xe, le, ge
+%! a = [-3   2
+%!       1   1];
+%!
+%! b = [ 0
+%!       1];
+%!
+%! c = [ 1  -1];
+%!
+%! r = 3;
+%!
+%! [x, l, g] = care (a, b, c.'*c, r);
+%!
+%! xe = [ 0.5895    1.8216
+%!        1.8216    8.8188];
+%!
+%! le = [-3.5026
+%!       -1.4370];
+%!
+%! ge = [ 0.6072    2.9396];
+%!
+%!assert (x, xe, 1e-4);
+%!assert (l, le, 1e-4);
+%!assert (g, ge, 1e-4);
+
+%!shared x, l, g, xe, le, ge
+%! a = [ 0.0  1.0
+%!       0.0  0.0];
+%!
+%! b = [ 0.0
+%!       1.0];
+%!
+%! c = [ 1.0  0.0
+%!       0.0  1.0
+%!       0.0  0.0];
+%!
+%! d = [ 0.0
+%!       0.0
+%!       1.0];
+%!
+%! [x, l, g] = care (a, b, c.'*c, d.'*d);
+%!
+%! xe = [ 1.7321   1.0000
+%!        1.0000   1.7321];
+%!
+%! le = [-0.8660 + 0.5000i
+%!       -0.8660 - 0.5000i];
+%!
+%! ge = [ 1.0000   1.7321];
+%!
+%!assert (x, xe, 1e-4);
+%!assert (l, le, 1e-4);
+%!assert (g, ge, 1e-4);
+
+%!shared x, xe
+%! a = [ 0.0  1.0
+%!       0.0  0.0 ];
+%!
+%! e = [ 1.0  0.0
+%!       0.0  1.0 ];
+%!
+%! b = [ 0.0
+%!       1.0 ];
+%!
+%! c = [ 1.0  0.0
+%!       0.0  1.0
+%!       0.0  0.0 ];
+%!
+%! d = [ 0.0
+%!       0.0
+%!       1.0 ];
+%!
+%! x = care (a, b, c.'*c, d.'*d, [], e);
+%!
+%! xe = [ 1.7321   1.0000
+%!        1.0000   1.7321 ];
+%!
+%!assert (x, xe, 1e-4);