/usr/share/octave/packages/control-3.0.0/dare.m is in octave-control 3.0.0-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 | ## Copyright (C) 2009-2015 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}] =} dare (@var{a}, @var{b}, @var{q}, @var{r})
## @deftypefnx {Function File} {[@var{x}, @var{l}, @var{g}] =} dare (@var{a}, @var{b}, @var{q}, @var{r}, @var{s})
## @deftypefnx {Function File} {[@var{x}, @var{l}, @var{g}] =} dare (@var{a}, @var{b}, @var{q}, @var{r}, @var{[]}, @var{e})
## @deftypefnx {Function File} {[@var{x}, @var{l}, @var{g}] =} dare (@var{a}, @var{b}, @var{q}, @var{r}, @var{s}, @var{e})
## Solve discrete-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 discrete-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'XA - X - A'XB (B'XB + R) B'XA + Q = 0
##
## -1
## A'XA - X - (A'XB + S) (B'XB + R) (B'XA + S') + Q = 0
##
## -1
## G = (B'XB + R) B'XA
##
## -1
## G = (B'XB + R) (B'XA + S')
##
## L = eig (A - B*G)
## @end group
## @end example
## @example
## @group
## -1
## A'XA - E'XE - A'XB (B'XB + R) B'XA + Q = 0
##
## -1
## A'XA - E'XE - (A'XB + S) (B'XB + R) (B'XA + S') + Q = 0
##
## -1
## G = (B'XB + R) B'XA
##
## -1
## G = (B'XB + R) (B'XA + 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{care, lqr, dlqr, kalman}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: October 2009
## Version: 0.5.1
function [x, l, g] = dare (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 ("dare: a, q, r must be real and square");
error ("dare: %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 ("dare: a and b must have the same number of rows");
error ("dare: %s and %s must have the same number of rows", ...
inputname (1), inputname (2));
endif
if (columns (r) != columns (b))
## error ("dare: b and r must have the same number of columns");
error ("dare: %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 ("dare: s(%dx%d) must be real and identically dimensioned with b(%dx%d)",
## rows (s), columns (s), rows (b), columns (b));
error ("dare: %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 ("dare: a and e must have the same number of rows");
error ("dare: %s and %s must have the same number of rows", ...
inputname (1), inputname (6));
endif
## check stabilizability
if (! isstabilizable (a, b, e, [], 1))
## error ("dare: (a, b) not stabilizable");
error ("dare: (%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 ("dare: require [q, s; s.', r] >= 0");
error ("dare: 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] = __sl_sb02od__ (a, b, q, r, b, true, false);
g = (r + b.'*x*b) \ (b.'*x*a); # gain matrix
else
[x, l] = __sl_sb02od__ (a, b, q, r, s, true, true);
g = (r + b.'*x*b) \ (b.'*x*a + s.'); # gain matrix
endif
else
if (isempty (s))
[x, l] = __sl_sg02ad__ (a, e, b, q, r, b, true, false);
g = (r + b.'*x*b) \ (b.'*x*a); # gain matrix
else
[x, l] = __sl_sg02ad__ (a, e, b, q, r, s, true, true);
g = (r + b.'*x*b) \ (b.'*x*a + s.'); # gain matrix
endif
endif
endfunction
%!shared x, l, g, xe, le, ge
%! a = [ 0.4 1.7
%! 0.9 3.8];
%!
%! b = [ 0.8
%! 2.1];
%!
%! c = [ 1 -1];
%!
%! r = 3;
%!
%! [x, l, g] = dare (a, b, c.'*c, r);
%!
%! xe = [ 1.5354 1.2623
%! 1.2623 10.5596];
%!
%! le = [-0.0022
%! 0.2454];
%!
%! ge = [ 0.4092 1.7283];
%!
%!assert (x, xe, 1e-4);
%!assert (sort (l), sort (le), 1e-4);
%!assert (g, ge, 1e-4);
## TODO: add more tests (nonempty s and/or e)
|