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1 ## Copyright (C) 1996, 1997 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 |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License 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, 59 Temple Place - Suite 330, Boston, MA |
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18 ## 02111-1307, USA. |
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19 |
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20 ## Usage: [k, p, e] = lqe (A, G, C, SigW, SigV {,Z}) |
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21 ## |
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22 ## Linear quadratic estimator (Kalman filter) design for the |
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23 ## continuous time system |
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24 ## |
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25 ## dx/dt = A x + B u + G w |
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26 ## y = C x + D u + v |
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27 ## |
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28 ## where w, v are zero-mean gaussian noise processes with respective |
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29 ## intensities SigW = cov (w, w) and SigV = cov (v, v). |
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30 ## |
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31 ## Z (if specified) is cov(w,v); otherwise cov(w,v) = 0. |
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32 ## |
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33 ## Observer structure is dz/dt = A z + B u + k( y - C z - D u). |
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34 ## |
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35 ## Returns: |
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36 ## |
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37 ## k = observer gain, (A - K C) is stable |
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38 ## p = solution of algebraic Riccati equation |
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39 ## e = closed loop poles of (A - K C) |
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40 |
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41 ## Author: A. S. Hodel <scotte@eng.auburn.edu> |
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42 ## Created: August 1993 |
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43 ## Adapted-By: jwe |
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44 |
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45 function [k, p, e] = lqe (a, g, c, sigw, sigv, zz) |
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46 |
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47 if (nargin != 5 && nargin != 6) |
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48 error ("lqe: invalid number of arguments"); |
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49 endif |
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50 |
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51 ## The problem is dual to the regulator design, so transform to lqr |
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52 ## call. |
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53 |
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54 if (nargin == 5) |
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55 [k, p, e] = lqr (a', c', g*sigw*g', sigv); |
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56 else |
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57 [k, p, e] = lqr (a', c', g*sigw*g', sigv, g*zz); |
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58 endif |
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59 |
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60 k = k'; |
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61 |
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62 endfunction |
