| 1 | function pmsm_ildp
|
|---|
| 2 | %verze ildp algoritmu s uvazovanim P (v logaritmu) pro PMSM motor
|
|---|
| 3 | tic
|
|---|
| 4 |
|
|---|
| 5 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|---|
| 6 | %pocatecni konstanty
|
|---|
| 7 |
|
|---|
| 8 | Iterace = 1; %iterace
|
|---|
| 9 | K = 20; %casy
|
|---|
| 10 | N = 50; %vzorky
|
|---|
| 11 |
|
|---|
| 12 | %konstanty motoru
|
|---|
| 13 | %Rs = 0.28;
|
|---|
| 14 | %Ls = 0.003465;
|
|---|
| 15 | %PSIpm = 0.1989;
|
|---|
| 16 | %kp = 1.5;
|
|---|
| 17 | %p = 4.0;
|
|---|
| 18 | %J = 0.04;
|
|---|
| 19 | DELTAt = 0.000125;
|
|---|
| 20 |
|
|---|
| 21 | %upravene konstanty
|
|---|
| 22 | Ca = 0.9898;
|
|---|
| 23 | Cb = 0.0072;
|
|---|
| 24 | Cc = 0.0361;
|
|---|
| 25 | Cd = 1.0;
|
|---|
| 26 | Ce = 0.0149;
|
|---|
| 27 |
|
|---|
| 28 | %omezeni rizeni
|
|---|
| 29 | cC1 = 100*100;
|
|---|
| 30 | cLb = -50;
|
|---|
| 31 | cUb = 50;
|
|---|
| 32 |
|
|---|
| 33 | %matice
|
|---|
| 34 | %kovariancni matice Q a R
|
|---|
| 35 | mQ = diag([0.0013 0.0013 5.0e-6 1.0e-10]);
|
|---|
| 36 | mR = diag([0.0006 0.0006]);
|
|---|
| 37 |
|
|---|
| 38 | mSigma = mR*mR';
|
|---|
| 39 |
|
|---|
| 40 | %matice pro vypocet
|
|---|
| 41 | %matice A zavisla na parametrech
|
|---|
| 42 | mA = zeros(4);
|
|---|
| 43 | mA(1,1) = Ca;
|
|---|
| 44 | mA(2,2) = Ca;
|
|---|
| 45 | mA(3,3) = Cd;
|
|---|
| 46 | mA(4,4) = 1;
|
|---|
| 47 | mA(4,3) = DELTAt;
|
|---|
| 48 |
|
|---|
| 49 | %macite C konstantni
|
|---|
| 50 | mC = [ 1 0 0 0; 0 1 0 0];
|
|---|
| 51 |
|
|---|
| 52 | %pozadovana hodnota otacek
|
|---|
| 53 | omega_t_stripe = 1.0015;
|
|---|
| 54 |
|
|---|
| 55 | %pocatecni hodnoty
|
|---|
| 56 | X0 = [0; 0; 1; pi/2];
|
|---|
| 57 | Y0 = [0; 0];
|
|---|
| 58 | P0 = diag([0.01 0.01 0.01 0.01]);
|
|---|
| 59 |
|
|---|
| 60 | h_bel = 0;
|
|---|
| 61 | h_beldx = [0; 0; 0; 0; 0; 0; 0; 0];
|
|---|
| 62 |
|
|---|
| 63 | %velikost okoli pro lokalni metodu
|
|---|
| 64 | rho = 0.5;
|
|---|
| 65 |
|
|---|
| 66 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|---|
| 67 | %globalni promenne
|
|---|
| 68 |
|
|---|
| 69 | Kpi_alfa = zeros(5, K); %konstanty aproximace slozky rizeni u_alfa
|
|---|
| 70 | Kpi_alfa(1, :) = (Cd - Cb*Ce)*ones(1, K);
|
|---|
| 71 | Kpi_alfa(2, :) = Ca*Ce*ones(1, K);
|
|---|
| 72 | Kpi_alfa(3, :) = Ca*Ce*ones(1, K);
|
|---|
| 73 | Kpi_alfa(4, :) = Cc*Ce*ones(1, K);
|
|---|
| 74 | Kpi_beta = zeros(5, K); %konstanty aproximace slozky rizeni u_beta
|
|---|
| 75 | Kpi_beta(1, :) = (Cd - Cb*Ce)*ones(1, K);
|
|---|
| 76 | Kpi_beta(2, :) = Ca*Ce*ones(1, K);
|
|---|
| 77 | Kpi_beta(3, :) = Ca*Ce*ones(1, K);
|
|---|
| 78 | Kpi_beta(4, :) = Cc*Ce*ones(1, K);
|
|---|
| 79 |
|
|---|
| 80 | Wv = zeros(35, K); %konstanty aproximace Bellmanovy fce
|
|---|
| 81 |
|
|---|
| 82 | Xkn = zeros(4, K, N); % X = [i_alfa, i_beta, omega, theta]
|
|---|
| 83 | Ykn = zeros(2, K, N); % Y = [i_alfa, i_beta]
|
|---|
| 84 | Pkn = zeros(4, 4, K, N); % P = N vzorku posloupnosti K matic 4x4
|
|---|
| 85 |
|
|---|
| 86 | mKy = zeros(4, 2); % K = pomocna matice pro vypocet
|
|---|
| 87 | mRy = zeros(2, 2); % R = pomocna matice pro vypocet
|
|---|
| 88 |
|
|---|
| 89 | Xstripe = zeros(4, K);
|
|---|
| 90 | Ystripe = zeros(4, K);
|
|---|
| 91 | Pstripe = zeros(4, 4, K);
|
|---|
| 92 |
|
|---|
| 93 | Epsilon = zeros(20, N); %globalni promena pro vypocet Bellmanovy fce z odchylek (X - Xprum)
|
|---|
| 94 |
|
|---|
| 95 | gka = 0; %globalni promenna pro prenos casu k
|
|---|
| 96 | gnu = 0; %globalni promenna pro prenos vzorku n
|
|---|
| 97 |
|
|---|
| 98 | Uopt2 = zeros(2, N);
|
|---|
| 99 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|---|
| 100 | %hlavni iteracni smycka
|
|---|
| 101 | for i = 1:Iterace,
|
|---|
| 102 |
|
|---|
| 103 | %generovani stavu
|
|---|
| 104 | for n = 1:N,
|
|---|
| 105 | Xkn(:, 1, n) = X0;
|
|---|
| 106 | Ykn(:, 1, n) = Y0 + mR * [randn(); randn()];
|
|---|
| 107 | Pkn(:, :, 1, n) = P0;
|
|---|
| 108 |
|
|---|
| 109 | for k = 1:K-1,
|
|---|
| 110 | Uk = uPi(k, Xkn(:, k, n), Pkn(:, :, k, n));
|
|---|
| 111 |
|
|---|
| 112 | mRy = mC * Pkn(:, :, k, n) * mC' + mR;
|
|---|
| 113 | mKy = Pkn(:, :, k, n) * mC' / mRy;
|
|---|
| 114 | Xkn(:, k+1, n) = fceG(Xkn(:, k, n), Uk) - mKy * (Ykn(:, k, n) - fceH(Xkn(:, k, n)));
|
|---|
| 115 | Ykn(:, k+1, n) = Xkn(1:2, k+1, n) + mR * [randn(); randn()]; %X kopie do Y + sum
|
|---|
| 116 | mA(1, 3) = Cb * sin(Xkn(4, k, n));
|
|---|
| 117 | mA(1, 4) = Cb * Xkn(3, k, n) * cos(Xkn(4, k, n));
|
|---|
| 118 | mA(2, 3) = - Cb * cos(Xkn(4, k, n));
|
|---|
| 119 | mA(2, 4) = Cb * Xkn(3, k, n) * sin(Xkn(4, k, n));
|
|---|
| 120 | mA(3, 1) = - Ce * sin(Xkn(4, k, n));
|
|---|
| 121 | mA(3, 2) = Ce * cos(Xkn(4, k, n));
|
|---|
| 122 | mA(3, 4) = - Ce * (Xkn(2, k, n) * sin(Xkn(4, k, n)) + Xkn(1, k, n) * cos(Xkn(4, k, n)));
|
|---|
| 123 | Pkn(:, :, k+1, n) = mA * (Pkn(:, :, k, n) - Pkn(:, :, k, n) * mC' * inv(mRy) * mC * Pkn(:, :, k, n)) * mA + mQ;
|
|---|
| 124 | end
|
|---|
| 125 | end
|
|---|
| 126 | Xstripe = mean(Xkn, 3);
|
|---|
| 127 | Ystripe = mean(Ykn, 3);
|
|---|
| 128 | Pstripe = mean(Pkn, 4);
|
|---|
| 129 |
|
|---|
| 130 | for k = K-1:-1:1,
|
|---|
| 131 | gka = k;
|
|---|
| 132 |
|
|---|
| 133 | % 1]
|
|---|
| 134 | for n = 1:N,
|
|---|
| 135 | %krive okoli
|
|---|
| 136 | Ykn(1, k, n) = Ykn(1, k, n) - Xkn(1, k, n);
|
|---|
| 137 | Ykn(2, k, n) = Ykn(2, k, n) - Xkn(2, k, n);
|
|---|
| 138 |
|
|---|
| 139 | Xkn(1, k, n) = Xstripe(1, k) + rho*randn();
|
|---|
| 140 | Xkn(2, k, n) = Xstripe(2, k) + rho*randn();
|
|---|
| 141 | Xkn(3, k, n) = Xstripe(3, k) + rho*randn();
|
|---|
| 142 | Xkn(4, k, n) = Xstripe(4, k) + rho*randn();
|
|---|
| 143 |
|
|---|
| 144 | Ykn(1, k, n) = Ykn(1, k, n) + Xkn(1, k, n);
|
|---|
| 145 | Ykn(2, k, n) = Ykn(2, k, n) + Xkn(2, k, n);
|
|---|
| 146 |
|
|---|
| 147 | Pkn(:, :, k, n) = Pstripe(:, :, k) .* exp(rho*randn(4));
|
|---|
| 148 | end
|
|---|
| 149 |
|
|---|
| 150 | % 2]
|
|---|
| 151 | for n = 1:N,
|
|---|
| 152 | gnu = n;
|
|---|
| 153 | [Uopt2(:, n), Hmin(n)] = fmincon(@Hamilt, uPi(k, Xkn(:, k, n),Pkn(:, :, k, n)), [], [], [], [], cLb, cUb, @Cond2, optimset('GradObj','on','GradConstr','on','Display','notify'));
|
|---|
| 154 | end
|
|---|
| 155 |
|
|---|
| 156 | % 3]
|
|---|
| 157 | for n = 1:N,
|
|---|
| 158 | Vn(n) = DELTAt*Hmin(n) + Vtilde(k+1, Xkn(:, k, n), Pkn(:, :, k, n));
|
|---|
| 159 | end
|
|---|
| 160 |
|
|---|
| 161 | % 4]
|
|---|
| 162 | Epsilon = zeros(8, N);
|
|---|
| 163 | for n = 1:N,
|
|---|
| 164 | Epsilon(1:4, n) = Xkn(1:4, k, n) - Xstripe(1:4, k);
|
|---|
| 165 | Epsilon(5:8, n) = diag(Pkn(:, :, k, n) ./ Pstripe(:, :, k));
|
|---|
| 166 | end
|
|---|
| 167 | mFi = matrixFi(Epsilon);
|
|---|
| 168 | FiFiTInvFi = (mFi*mFi')\mFi;
|
|---|
| 169 | Wv(:,k) = FiFiTInvFi * Vn';
|
|---|
| 170 |
|
|---|
| 171 | for n = 1:N,
|
|---|
| 172 | tialfa(n) = Xkn(1, k, n);
|
|---|
| 173 | tibeta(n) = Xkn(2, k, n);
|
|---|
| 174 | tomega(n) = Xkn(3, k, n);
|
|---|
| 175 | ttheta(n) = Xkn(4, k, n);
|
|---|
| 176 | end
|
|---|
| 177 | mPsi = [tomega',...
|
|---|
| 178 | -tialfa'.*sin(ttheta)',...
|
|---|
| 179 | tibeta'.*cos(ttheta)',...
|
|---|
| 180 | -Uopt2(1,:)'.*sin(ttheta)',...
|
|---|
| 181 | ones(N,1)];
|
|---|
| 182 | PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
|
|---|
| 183 | Kpi_alfa(:, k) = PsiPsiTInvPsi * (omega_t_stripe * ones(N, 1));
|
|---|
| 184 |
|
|---|
| 185 | mPsi = [tomega',...
|
|---|
| 186 | -tialfa'.*sin(ttheta)',...
|
|---|
| 187 | tibeta'.*cos(ttheta)',...
|
|---|
| 188 | Uopt2(2,:)'.*cos(ttheta)',...
|
|---|
| 189 | ones(N,1)];
|
|---|
| 190 | PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
|
|---|
| 191 | Kpi_beta(:, k) = PsiPsiTInvPsi * (omega_t_stripe * ones(N, 1));
|
|---|
| 192 | end
|
|---|
| 193 | end
|
|---|
| 194 |
|
|---|
| 195 | %%%%%%%%%%%
|
|---|
| 196 | toc
|
|---|
| 197 | % keyboard
|
|---|
| 198 |
|
|---|
| 199 | %vykresleni grafu
|
|---|
| 200 | % clf
|
|---|
| 201 | Ukn = zeros(2, K, N);
|
|---|
| 202 | for n = 1:N,
|
|---|
| 203 | Xkn(:, 1, n) = X0;
|
|---|
| 204 | Ykn(:, 1, n) = Y0 + mR * [randn(); randn()];
|
|---|
| 205 | Pkn(:, :, 1, n) = P0;
|
|---|
| 206 | for k = 1:K-1,
|
|---|
| 207 | Ukn(:, k, n) = uPi(k, Xkn(:, k, n), Pkn(:, :, k, n));
|
|---|
| 208 | mRy = mC * Pkn(:, :, k, n) * mC' + mR;
|
|---|
| 209 | mKy = Pkn(:, :, k, n) * mC' / mRy;
|
|---|
| 210 | Xkn(:, k+1, n) = fceG(Xkn(:, k, n), Ukn(:, k, n)) - mKy * (Ykn(:, k, n) - fceH(Xkn(:, k, n)));
|
|---|
| 211 | Ykn(:, k+1, n) = Xkn(1:2, k+1, n) + mR * [randn(); randn()]; %X kopie do Y + sum
|
|---|
| 212 | mA(1, 3) = Cb * sin(Xkn(4, k, n));
|
|---|
| 213 | mA(1, 4) = Cb * Xkn(3, k, n) * cos(Xkn(4, k, n));
|
|---|
| 214 | mA(2, 3) = - Cb * cos(Xkn(4, k, n));
|
|---|
| 215 | mA(2, 4) = Cb * Xkn(3, k, n) * sin(Xkn(4, k, n));
|
|---|
| 216 | mA(3, 1) = - Ce * sin(Xkn(4, k, n));
|
|---|
| 217 | mA(3, 2) = Ce * cos(Xkn(4, k, n));
|
|---|
| 218 | mA(3, 4) = - Ce * (Xkn(2, k, n) * sin(Xkn(4, k, n)) + Xkn(1, k, n) * cos(Xkn(4, k, n)));
|
|---|
| 219 | Pkn(:, :, k+1, n) = mA * (Pkn(:, :, k, n) - Pkn(:, :, k, n) * mC' * inv(mRy) * mC * Pkn(:, :, k, n)) * mA + mQ;
|
|---|
| 220 | end
|
|---|
| 221 |
|
|---|
| 222 | hold all
|
|---|
| 223 | subplot(3,4,1);
|
|---|
| 224 | title('X:i_{\alpha}')
|
|---|
| 225 | plot(1:K,Xkn(1,:,n))
|
|---|
| 226 |
|
|---|
| 227 | hold all
|
|---|
| 228 | subplot(3,4,2);
|
|---|
| 229 | title('X:i_{\beta}')
|
|---|
| 230 | plot(1:K,Xkn(2,:,n))
|
|---|
| 231 |
|
|---|
| 232 | hold all
|
|---|
| 233 | subplot(3,4,3);
|
|---|
| 234 | title('X:\omega')
|
|---|
| 235 | plot(1:K,Xkn(3,:,n))
|
|---|
| 236 |
|
|---|
| 237 | hold all
|
|---|
| 238 | subplot(3,4,4);
|
|---|
| 239 | title('X:\theta')
|
|---|
| 240 | plot(1:K,Xkn(4,:,n))
|
|---|
| 241 |
|
|---|
| 242 | hold all
|
|---|
| 243 | subplot(3,4,5);
|
|---|
| 244 | title('Y:i_{\alpha}')
|
|---|
| 245 | plot(1:K,Ykn(1,:,n))
|
|---|
| 246 |
|
|---|
| 247 | hold all
|
|---|
| 248 | subplot(3,4,6);
|
|---|
| 249 | title('Y:i_{\beta}')
|
|---|
| 250 | plot(1:K,Xkn(1,:,n))
|
|---|
| 251 |
|
|---|
| 252 | hold all
|
|---|
| 253 | subplot(3,4,7);
|
|---|
| 254 | title('u_{\alpha}')
|
|---|
| 255 | plot(1:K,Ukn(1,:,n))
|
|---|
| 256 |
|
|---|
| 257 | hold all
|
|---|
| 258 | subplot(3,4,8);
|
|---|
| 259 | title('u_{\beta}')
|
|---|
| 260 | plot(1:K,Ukn(2,:,n))
|
|---|
| 261 |
|
|---|
| 262 | hold all
|
|---|
| 263 | subplot(3,4,9);
|
|---|
| 264 | title('P(1, 1)')
|
|---|
| 265 | plot(1:K,squeeze(Pkn(1, 1, :, n)))
|
|---|
| 266 |
|
|---|
| 267 | hold all
|
|---|
| 268 | subplot(3,4,10);
|
|---|
| 269 | title('P(2, 2)')
|
|---|
| 270 | plot(1:K,squeeze(Pkn(2, 2, :, n)))
|
|---|
| 271 |
|
|---|
| 272 | hold all
|
|---|
| 273 | subplot(3,4,11);
|
|---|
| 274 | title('P(3, 3)')
|
|---|
| 275 | plot(1:K,squeeze(Pkn(3, 3, :, n)))
|
|---|
| 276 |
|
|---|
| 277 | hold all
|
|---|
| 278 | subplot(3,4,12);
|
|---|
| 279 | title('P(4, 4)')
|
|---|
| 280 | plot(1:K,squeeze(Pkn(4, 4, :, n)))
|
|---|
| 281 | end
|
|---|
| 282 |
|
|---|
| 283 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|---|
| 284 | %pomocne funkce
|
|---|
| 285 |
|
|---|
| 286 | function [val_uPi] = uPi(k_uPi, x_uPi, p_uPi)
|
|---|
| 287 | val_uPi = zeros(2, 1);
|
|---|
| 288 | val_uPi(1) = (-omega_t_stripe + Kpi_alfa(1, k_uPi)*x_uPi(3) - Kpi_alfa(2, k_uPi)*x_uPi(1)*sin(x_uPi(4)) + Kpi_alfa(3, k_uPi)*x_uPi(2)*cos(x_uPi(4)) + Kpi_alfa(5)) / (Kpi_alfa(4)*sin(x_uPi(4)));
|
|---|
| 289 | val_uPi(2) = ( omega_t_stripe - Kpi_beta(1, k_uPi)*x_uPi(3) + Kpi_beta(2, k_uPi)*x_uPi(1)*sin(x_uPi(4)) - Kpi_beta(3, k_uPi)*x_uPi(2)*cos(x_uPi(4)) - Kpi_beta(5)) / (Kpi_beta(4)*cos(x_uPi(4)));
|
|---|
| 290 |
|
|---|
| 291 | if (val_uPi(1)<cLb)
|
|---|
| 292 | val_uPi(1) = cLb;
|
|---|
| 293 | end
|
|---|
| 294 | if (val_uPi(1)>cUb)
|
|---|
| 295 | val_uPi(1) = cUb;
|
|---|
| 296 | end
|
|---|
| 297 | if (val_uPi(2)<cLb)
|
|---|
| 298 | val_uPi(2) = cLb;
|
|---|
| 299 | end
|
|---|
| 300 | if (val_uPi(2)>cUb)
|
|---|
| 301 | val_uPi(2) = cUb;
|
|---|
| 302 | end
|
|---|
| 303 | end
|
|---|
| 304 |
|
|---|
| 305 | function [val_ham, val_grad] = Hamilt(u_ham) %u_ham = vect(2,1)
|
|---|
| 306 | % val_ham = (Xkn(1, gka, gnu) + Xkn(2, gka, gnu)*u_ham - Rk(gka+1))^2 + Xkn(3, gka, gnu)*u_ham^2 ... + sigma^2 ... %ztrata l
|
|---|
| 307 | % + [Xkn(2, gka, gnu)*u_ham; ...
|
|---|
| 308 | % Xkn(3, gka, gnu)*u_ham*(Xkn(1, gka+1, gnu) - Xkn(1, gka, gnu) - Xkn(2, gka, gnu)*u_ham)/(Xkn(3, gka, gnu)*u_ham^2 + sigma^2); ...
|
|---|
| 309 | % -Xkn(3, gka, gnu)^2*u_ham^2/(Xkn(3, gka, gnu)*u_ham^2 + sigma^2)]' ... %fce f
|
|---|
| 310 | % *Vtilde_dx(gka+1, Xkn(:, gka, gnu)) ...
|
|---|
| 311 | % + Wv(5, gka+1)*sigma;
|
|---|
| 312 |
|
|---|
| 313 | loss = (Xkn(3, gka, gnu) - omega_t_stripe)^2;
|
|---|
| 314 |
|
|---|
| 315 | mRy = mC * Pkn(:, :, gka, gnu) * mC' + mR;
|
|---|
| 316 | mKy = Pkn(:, :, gka, gnu) * mC' / mRy;
|
|---|
| 317 | tXkn = fceG(Xkn(:, gka, gnu), u_ham) - mKy * (Ykn(:, gka, gnu) - fceH(Xkn(:, gka, gnu)));
|
|---|
| 318 | mA(1, 3) = Cb * sin(Xkn(4, gka, gnu));
|
|---|
| 319 | mA(1, 4) = Cb * Xkn(3, gka, gnu) * cos(Xkn(4, gka, gnu));
|
|---|
| 320 | mA(2, 3) = - Cb * cos(Xkn(4, gka, gnu));
|
|---|
| 321 | mA(2, 4) = Cb * Xkn(3, gka, gnu) * sin(Xkn(4, gka, gnu));
|
|---|
| 322 | mA(3, 1) = - Ce * sin(Xkn(4, gka, gnu));
|
|---|
| 323 | mA(3, 2) = Ce * cos(Xkn(4, gka, gnu));
|
|---|
| 324 | mA(3, 4) = - Ce * (Xkn(2, gka, gnu) * sin(Xkn(4, gka, gnu)) + Xkn(1, gka, gnu) * cos(Xkn(4, gka, gnu)));
|
|---|
| 325 | tPkn = mA * (Pkn(:, :, gka, gnu) - Pkn(:, :, gka, gnu) * mC' * inv(mRy) * mC * Pkn(:, :, gka, gnu)) * mA + mQ;
|
|---|
| 326 | tf = zeros(8,1);
|
|---|
| 327 | tf(1:4) = tXkn;
|
|---|
| 328 | tf(5:8) = diag(tPkn);
|
|---|
| 329 |
|
|---|
| 330 | val_ham = loss + tf' * Vtilde_dx(gka+1, Xkn(:, gka, gnu), Pkn(:, :, gka, gnu)) + 1/2 * trace(mSigma * ( Wv(10, gka+1)*[2 0; 0 0] + Wv(18, gka+1)*[0 0; 0 2] ));
|
|---|
| 331 |
|
|---|
| 332 | tfdu = zeros(8,2);
|
|---|
| 333 | tXkn = fceG_du(Xkn(:, gka, gnu), u_ham);
|
|---|
| 334 | tfdu(1:4,:) = tXkn;
|
|---|
| 335 |
|
|---|
| 336 | val_grad = tfdu' * Vtilde_dx(gka+1, Xkn(:, gka, gnu), Pkn(:, :, gka, gnu));
|
|---|
| 337 | % val_grad = 2*(Xkn(1, gka, gnu) + Xkn(2, gka, gnu)*u_ham - Rk(gka+1))*Xkn(2, gka, gnu) + 2*Xkn(3, gka, gnu)*u_ham ... %ztrata du
|
|---|
| 338 | % + [Xkn(2, gka, gnu);...
|
|---|
| 339 | % (2*u_ham^2*Xkn(3, gka, gnu)^2*(Xkn(1, gka, gnu) - Xkn(1, gka+1, gnu) + u_ham*Xkn(2, gka, gnu)))/(sigma^2 + u_ham^2*Xkn(3, gka, gnu))^2 - (u_ham*Xkn(2, gka, gnu)*Xkn(3, gka, gnu))/(sigma^2 + u_ham^2*Xkn(3, gka, gnu)) - (Xkn(3, gka, gnu)*(Xkn(1, gka, gnu) - Xkn(1, gka+1, gnu) + u_ham*Xkn(2, gka, gnu)))/(sigma^2 + u_ham^2*Xkn(3, gka, gnu));...
|
|---|
| 340 | % (2*u_ham^3*Xkn(3, gka, gnu)^3)/(sigma^2 + u_ham^2*Xkn(3, gka, gnu))^2 - (2*u_ham*Xkn(3, gka, gnu)^2)/(sigma^2 + u_ham^2*Xkn(3, gka, gnu))]' ... %fce f du
|
|---|
| 341 | % * Vtilde_dx(gka+1, Xkn(:, gka, gnu)); %derivace Bellman fce
|
|---|
| 342 | end
|
|---|
| 343 |
|
|---|
| 344 | function [val_Vt] = Vtilde(k_Vt, x_Vt, p_Vt)
|
|---|
| 345 | if(k_Vt == K)
|
|---|
| 346 | val_Vt = h_bel;
|
|---|
| 347 | else
|
|---|
| 348 | Epsl = zeros(8, 1);
|
|---|
| 349 | Epsl(1:4) = x_Vt(1:4) - Xstripe(1:4, k_Vt);
|
|---|
| 350 | Epsl(5:8) = diag(p_Vt ./ Pstripe(:, :, k));
|
|---|
| 351 |
|
|---|
| 352 | val_Vt = vectFi(Epsl)' * Wv(:,k_Vt);
|
|---|
| 353 | end
|
|---|
| 354 | end
|
|---|
| 355 |
|
|---|
| 356 | function [val_Vt] = Vtilde_dx(k_Vt, x_Vt, p_Vt)
|
|---|
| 357 | if(k_Vt == K)
|
|---|
| 358 | val_Vt = h_beldx;
|
|---|
| 359 | else
|
|---|
| 360 | Epsl = zeros(8, 1);
|
|---|
| 361 | Epsl(1:4) = x_Vt(1:4) - Xstripe(1:4, k_Vt);
|
|---|
| 362 | Epsl(5:8) = diag(p_Vt ./ Pstripe(:, :, k));
|
|---|
| 363 |
|
|---|
| 364 | val_Vt = difFi(Epsl)' * Wv(:,k_Vt);
|
|---|
| 365 | end
|
|---|
| 366 | end
|
|---|
| 367 |
|
|---|
| 368 | function [val_Fi] = vectFi(x_Fi)
|
|---|
| 369 | val_Fi = [ ...
|
|---|
| 370 | 1; ... %1
|
|---|
| 371 | x_Fi(1); ... %Xi pro 1-4
|
|---|
| 372 | x_Fi(2); ...
|
|---|
| 373 | x_Fi(3); ...
|
|---|
| 374 | x_Fi(4); ...
|
|---|
| 375 | log(x_Fi(5)); ... %ln Xi pro 5-8 tj diagonala matice Pt 4x4
|
|---|
| 376 | log(x_Fi(6)); ...
|
|---|
| 377 | log(x_Fi(7)); ...
|
|---|
| 378 | log(x_Fi(8)); ...
|
|---|
| 379 | x_Fi(1)^2; ... %kvadraticke cleny jen v Xi 1-4 a kombinovane
|
|---|
| 380 | x_Fi(1)*x_Fi(2); ...
|
|---|
| 381 | x_Fi(1)*x_Fi(3); ...
|
|---|
| 382 | x_Fi(1)*x_Fi(4); ...
|
|---|
| 383 | x_Fi(1)*log(x_Fi(5)); ...
|
|---|
| 384 | x_Fi(1)*log(x_Fi(6)); ...
|
|---|
| 385 | x_Fi(1)*log(x_Fi(7)); ...
|
|---|
| 386 | x_Fi(1)*log(x_Fi(8)); ...
|
|---|
| 387 | x_Fi(2)^2; ...
|
|---|
| 388 | x_Fi(2)*x_Fi(3); ...
|
|---|
| 389 | x_Fi(2)*x_Fi(4); ...
|
|---|
| 390 | x_Fi(2)*log(x_Fi(5)); ...
|
|---|
| 391 | x_Fi(2)*log(x_Fi(6)); ...
|
|---|
| 392 | x_Fi(2)*log(x_Fi(7)); ...
|
|---|
| 393 | x_Fi(2)*log(x_Fi(8)); ...
|
|---|
| 394 | x_Fi(3)^2; ...
|
|---|
| 395 | x_Fi(3)*x_Fi(4); ...
|
|---|
| 396 | x_Fi(3)*log(x_Fi(5)); ...
|
|---|
| 397 | x_Fi(3)*log(x_Fi(6)); ...
|
|---|
| 398 | x_Fi(3)*log(x_Fi(7)); ...
|
|---|
| 399 | x_Fi(3)*log(x_Fi(8)); ...
|
|---|
| 400 | x_Fi(4)^2; ...
|
|---|
| 401 | x_Fi(4)*log(x_Fi(5)); ...
|
|---|
| 402 | x_Fi(4)*log(x_Fi(6)); ...
|
|---|
| 403 | x_Fi(4)*log(x_Fi(7)); ...
|
|---|
| 404 | x_Fi(4)*log(x_Fi(8)); ...
|
|---|
| 405 | ];
|
|---|
| 406 | end
|
|---|
| 407 |
|
|---|
| 408 | function [val_Fi] = matrixFi(x_Fi)
|
|---|
| 409 | val_Fi = [ ...
|
|---|
| 410 | ones(1, N); ... %1
|
|---|
| 411 | x_Fi(1, :); ... %Xi pro 1-4
|
|---|
| 412 | x_Fi(2, :); ...
|
|---|
| 413 | x_Fi(3, :); ...
|
|---|
| 414 | x_Fi(4, :); ...
|
|---|
| 415 | log(x_Fi(5, :)); ... %ln Xi pro 5-8 tj diagonala matice Pt 4x4
|
|---|
| 416 | log(x_Fi(6, :)); ...
|
|---|
| 417 | log(x_Fi(7, :)); ...
|
|---|
| 418 | log(x_Fi(8, :)); ...
|
|---|
| 419 | x_Fi(1, :).^2; ... %kvadraticke cleny jen v Xi 1-4 a kombinovane
|
|---|
| 420 | x_Fi(1, :).*x_Fi(2, :); ...
|
|---|
| 421 | x_Fi(1, :).*x_Fi(3, :); ...
|
|---|
| 422 | x_Fi(1, :).*x_Fi(4, :); ...
|
|---|
| 423 | x_Fi(1, :).*log(x_Fi(5, :)); ...
|
|---|
| 424 | x_Fi(1, :).*log(x_Fi(6, :)); ...
|
|---|
| 425 | x_Fi(1, :).*log(x_Fi(7, :)); ...
|
|---|
| 426 | x_Fi(1, :).*log(x_Fi(8, :)); ...
|
|---|
| 427 | x_Fi(2, :).^2; ...
|
|---|
| 428 | x_Fi(2, :).*x_Fi(3, :); ...
|
|---|
| 429 | x_Fi(2, :).*x_Fi(4, :); ...
|
|---|
| 430 | x_Fi(2, :).*log(x_Fi(5, :)); ...
|
|---|
| 431 | x_Fi(2, :).*log(x_Fi(6, :)); ...
|
|---|
| 432 | x_Fi(2, :).*log(x_Fi(7, :)); ...
|
|---|
| 433 | x_Fi(2, :).*log(x_Fi(8, :)); ...
|
|---|
| 434 | x_Fi(3, :).^2; ...
|
|---|
| 435 | x_Fi(3, :).*x_Fi(4, :); ...
|
|---|
| 436 | x_Fi(3, :).*log(x_Fi(5, :)); ...
|
|---|
| 437 | x_Fi(3, :).*log(x_Fi(6, :)); ...
|
|---|
| 438 | x_Fi(3, :).*log(x_Fi(7, :)); ...
|
|---|
| 439 | x_Fi(3, :).*log(x_Fi(8, :)); ...
|
|---|
| 440 | x_Fi(4, :).^2; ...
|
|---|
| 441 | x_Fi(4, :).*log(x_Fi(5, :)); ...
|
|---|
| 442 | x_Fi(4, :).*log(x_Fi(6, :)); ...
|
|---|
| 443 | x_Fi(4, :).*log(x_Fi(7, :)); ...
|
|---|
| 444 | x_Fi(4, :).*log(x_Fi(8, :)); ...
|
|---|
| 445 | ];
|
|---|
| 446 |
|
|---|
| 447 | end
|
|---|
| 448 |
|
|---|
| 449 | function [val_Fi] = difFi(x_Fi)
|
|---|
| 450 | val_Fi = [ ...
|
|---|
| 451 | 0 0 0 0 0 0 0 0; ...
|
|---|
| 452 | 1 0 0 0 0 0 0 0; ...
|
|---|
| 453 | 0 1 0 0 0 0 0 0; ...
|
|---|
| 454 | 0 0 1 0 0 0 0 0; ...
|
|---|
| 455 | 0 0 0 1 0 0 0 0; ...
|
|---|
| 456 | 0 0 0 0 1/x_Fi(5) 0 0 0; ...
|
|---|
| 457 | 0 0 0 0 0 1/x_Fi(6) 0 0; ...
|
|---|
| 458 | 0 0 0 0 0 0 1/x_Fi(7) 0; ...
|
|---|
| 459 | 0 0 0 0 0 0 0 1/x_Fi(8); ...
|
|---|
| 460 | 2*x_Fi(1) 0 0 0 0 0 0 0; ...
|
|---|
| 461 | x_Fi(2) x_Fi(1) 0 0 0 0 0 0; ...
|
|---|
| 462 | x_Fi(3) 0 x_Fi(1) 0 0 0 0 0; ...
|
|---|
| 463 | x_Fi(4) 0 0 x_Fi(1) 0 0 0 0; ...
|
|---|
| 464 | log(x_Fi(5)) 0 0 0 x_Fi(1)/x_Fi(5) 0 0 0; ...
|
|---|
| 465 | log(x_Fi(6)) 0 0 0 0 x_Fi(1)/x_Fi(6) 0 0; ...
|
|---|
| 466 | log(x_Fi(7)) 0 0 0 0 0 x_Fi(1)/x_Fi(7) 0; ...
|
|---|
| 467 | log(x_Fi(8)) 0 0 0 0 0 0 x_Fi(1)/x_Fi(8); ...
|
|---|
| 468 | 0 2*x_Fi(2) 0 0 0 0 0 0; ...
|
|---|
| 469 | 0 x_Fi(3) x_Fi(2) 0 0 0 0 0; ...
|
|---|
| 470 | 0 x_Fi(4) 0 x_Fi(2) 0 0 0 0; ...
|
|---|
| 471 | 0 log(x_Fi(5)) 0 0 x_Fi(2)/x_Fi(5) 0 0 0; ...
|
|---|
| 472 | 0 log(x_Fi(6)) 0 0 0 x_Fi(2)/x_Fi(6) 0 0; ...
|
|---|
| 473 | 0 log(x_Fi(7)) 0 0 0 0 x_Fi(2)/x_Fi(7) 0; ...
|
|---|
| 474 | 0 log(x_Fi(8)) 0 0 0 0 0 x_Fi(2)/x_Fi(8); ...
|
|---|
| 475 | 0 0 2*x_Fi(3) 0 0 0 0 0; ...
|
|---|
| 476 | 0 0 x_Fi(4) x_Fi(3) 0 0 0 0; ...
|
|---|
| 477 | 0 0 log(x_Fi(5)) 0 x_Fi(3)/x_Fi(5) 0 0 0; ...
|
|---|
| 478 | 0 0 log(x_Fi(6)) 0 0 x_Fi(3)/x_Fi(6) 0 0; ...
|
|---|
| 479 | 0 0 log(x_Fi(7)) 0 0 0 x_Fi(3)/x_Fi(7) 0; ...
|
|---|
| 480 | 0 0 log(x_Fi(8)) 0 0 0 0 x_Fi(3)/x_Fi(8); ...
|
|---|
| 481 | 0 0 0 2*x_Fi(4) 0 0 0 0; ...
|
|---|
| 482 | 0 0 0 log(x_Fi(5)) x_Fi(4)/x_Fi(5) 0 0 0; ...
|
|---|
| 483 | 0 0 0 log(x_Fi(6)) 0 x_Fi(4)/x_Fi(6) 0 0; ...
|
|---|
| 484 | 0 0 0 log(x_Fi(7)) 0 0 x_Fi(4)/x_Fi(7) 0; ...
|
|---|
| 485 | 0 0 0 log(x_Fi(8)) 0 0 0 x_Fi(4)/x_Fi(8); ...
|
|---|
| 486 | ];
|
|---|
| 487 | end
|
|---|
| 488 |
|
|---|
| 489 | function [c, ceq, GC, GCeq] = Cond2(x)
|
|---|
| 490 | c = x(1)*x(1) + x(2)*x(2) - cC1;
|
|---|
| 491 | ceq = [];
|
|---|
| 492 | GC = [2*x(1); 2*x(2)];
|
|---|
| 493 | GCeq = [];
|
|---|
| 494 | end
|
|---|
| 495 |
|
|---|
| 496 | function [x_ret] = fceG(x_in, u_in)
|
|---|
| 497 | x_ret = zeros(4, 1);
|
|---|
| 498 | x_ret(1) = Ca * x_in(1) + Cb * x_in(3) * sin(x_in(4)) + Cc * u_in(1);
|
|---|
| 499 | x_ret(2) = Ca * x_in(2) - Cb * x_in(3) * cos(x_in(4)) + Cc * u_in(2);
|
|---|
| 500 | x_ret(3) = Cd * x_in(3) + Ce * (x_in(2) * cos(x_in(4)) - x_in(1) * sin(x_in(4)));
|
|---|
| 501 | x_ret(4) = x_in(4) + x_in(3) * DELTAt;
|
|---|
| 502 | end
|
|---|
| 503 |
|
|---|
| 504 | function [x_ret] = fceG_du(x_in, u_in)
|
|---|
| 505 | x_ret = zeros(4, 2);
|
|---|
| 506 | x_ret(1, 1) = Cc;
|
|---|
| 507 | x_ret(2, 2) = Cc;
|
|---|
| 508 | end
|
|---|
| 509 |
|
|---|
| 510 | function [y_ret] = fceH(x_in)
|
|---|
| 511 | y_ret = zeros(2, 1);
|
|---|
| 512 | y_ret(1) = x_in(1);
|
|---|
| 513 | y_ret(2) = x_in(2);
|
|---|
| 514 | end
|
|---|
| 515 |
|
|---|
| 516 | end
|
|---|
