Mercurial > hg > octave-lojdl
changeset 74:1b1a6414f9ed
[project @ 1993-08-30 15:07:26 by jwe]
Initial revision
author | jwe |
---|---|
date | Mon, 30 Aug 1993 15:07:26 +0000 |
parents | f3c9042fd609 |
children | 505c8b681f66 |
files | scripts/control/dare.m |
diffstat | 1 files changed, 94 insertions(+), 0 deletions(-) [+] |
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new file mode 100644 --- /dev/null +++ b/scripts/control/dare.m @@ -0,0 +1,94 @@ +function x = dare (a, b, c, r, opt) + +# Usage: x = dare (a, b, c, r {,opt}) +# +# Solves discrete-time algebraic riccati equation +# +# a' x a - x + a' x b (r + b' x b)^{-1} b' x a + c = 0 +# +# for +# +# a: nxn +# b: nxm +# c: nxn, symmetric positive semidefinite +# r: mxm, invertible +# +# If c is not square, then the function attempts to use c'*c instead. +# +# Solution method: Laub's Schur method (IEEE Trans Auto Contr, 1979) applied +# to the appropriate symplectic matrix. +# +# See also: Ran and Rodman, "Stable Hermitian Solutions of Discrete +# Algebraic Riccati Equations," Mathematics of Control, Signals and +# Systems, Vol 5, no 2 (1992) pp 165-194. +# +# opt is an option passed to the eigenvalue balancing routine default +# is "B". +# +# See also: balance, are + +# Written by A. S. Hodel (scotte@eng.auburn.edu) August 1993. + + if (nargin == 4 || nargin == 5) + if (nargin == 5) + if (opt != "N" || opt != "P" || opt != "S" || opt != "B") + fprintf (stderr, "dare: opt has an illegal value -- setting to B"); + opt = "B"; + endif + else + opt = "B"; + endif + +# Check a matrix dimensions + if ((n = is_square (a)) == 0) + error ("dare: a is not square"); + endif + +# Check a,b compatibility. + + [n1, m] = size (b); + + if (n1 != n) + fprintf (stderr, "warning: dare: a,b are not conformable"); + endif + + if (is_controllable (a, b) == 0) + fprintf ("warning: dare: a,b are not controllable"); + endif + +# Check a,c compatibility. + + if (is_observable (a, c) == 0) + fprintf (stderr "warning: dare: a,c are not observable"); + endif + + if ((p = is_square (c)) == 0) + c = c'*c; + p = rows (c); + endif + + if (n != p) + error ("dare: a,c are not conformable"); + endif + +# Check r dimensions. + + if ((m1 = is_square (r)) == 0) + fprintf("warning: dare: r is not square"); + elseif (m1 != m) + fprintf(stderr, "warning: b,r are not conformable"); + endif + + brb = (b/r)*b'; + atc = a'\c; + [d, sy] = balance ([a + brb*atc, -brb/(a'); -atc, inv (a')], opt); + [u, s] = schur(sy,'D'); + u = d*u; + n1 = n+1; + n2 = 2*n; + x = u (n1:n2, 1:n)/u(1:n, 1:n); + else + error ("usage: x = dare (a, b, c, r {,opt})"); + endif + +endfunction