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[project @ 1993-12-03 02:00:15 by jwe]
author jwe
date Fri, 03 Dec 1993 02:00:15 +0000
parents c69be6819009
children 9a17c682207e
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1 # Copyright (C) 1993 John W. Eaton
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2 #
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3 # This file is part of Octave.
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4 #
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5 # Octave is free software; you can redistribute it and/or modify it
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6 # under the terms of the GNU General Public License as published by the
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7 # Free Software Foundation; either version 2, or (at your option) any
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8 # later version.
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9 #
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10 # Octave is distributed in the hope that it will be useful, but WITHOUT
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11 # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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12 # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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13 # for more details.
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14 #
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15 # You should have received a copy of the GNU General Public License
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16 # along with Octave; see the file COPYING. If not, write to the Free
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17 # Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
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18
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19 function [k, p, e] = lqe (a, g, c, sigw, sigv, zz)
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20
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21 # Usage: [k, p, e] = lqe (A, G, C, SigW, SigV {,Z})
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22 #
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23 # Linear quadratic estimator (Kalman filter) design for the
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24 # continuous time system
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25 #
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26 # dx/dt = A x + B u + G w
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27 # y = C x + D u + w
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28 #
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29 # where w, v are zero-mean gaussian noise processes with respective
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30 # intensities SigW = cov (w, w) and SigV = cov (v, v).
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31 #
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32 # Z (if specified) is cov(w,v); otherwise cov(w,v) = 0.
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33 #
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34 # Observer structure is dz/dt = A z + B u + k( y - C z - D u).
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35 #
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36 # Returns:
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37 #
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38 # k = observer gain, (A - K C) is stable
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39 # p = solution of algebraic Riccati equation
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40 # e = closed loop poles of (A - K C)
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41
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42 # Written by A. S. Hodel (scotte@eng.auburn.edu) August, 1993.
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43
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44 if (nargin != 5 && nargin != 6)
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45 error ("lqe: illegal number of arguments");
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46 endif
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47
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48 # The problem is dual to the regulator design, so transform to lqr
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49 # call.
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50
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51 if (nargin == 5)
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52 [k, p, e] = lqr (a', c', g*sigw*g', sigv);
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53 else
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54 [k, p, e] = lqr (a', c', g*sigw*g', sigv, g*zz);
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55 endif
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56
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57 endfunction