| 1 | function ildp
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| 2 |
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| 3 | tic
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| 4 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 5 | %pocatecni konstanty
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| 6 |
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| 7 | Iterace = 2; %iterace
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| 8 | K = 20; %casy
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| 9 | N = 50; %vzorky
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| 10 |
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| 11 | sigma = 1;
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| 12 | Sigmas = [[sigma^2 0 0]; [0 0 0]; [0 0 0]];
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| 13 |
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| 14 | h = 0;
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| 15 | hdx = [0; 0; 0];
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| 16 | hdxdx = [[0 0 0]; [0 0 0]; [0 0 0]];
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| 17 |
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| 18 | Rk = ones(1, K);
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| 19 | x0 = [0; 0; 1];
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| 20 |
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| 21 | %velikost okoli pro lokalni metodu
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| 22 | rho = 5;
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| 23 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 24 | %globalni promenne
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| 25 |
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| 26 | Kpi = ones(4, K);
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| 27 | Kpi(4, :) = zeros(1, K);
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| 28 |
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| 29 | Wv = zeros(10, K);
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| 30 |
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| 31 | Xkn = zeros(3, K, N);
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| 32 | Xstripe = zeros(3, K);
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| 33 |
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| 34 | gka = 0;
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| 35 | gnu = 0;
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| 36 |
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| 37 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 38 | %iteracni smycka
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| 39 | % clf reset
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| 40 |
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| 41 | % PtMin = 0.0001;
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| 42 |
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| 43 | % UU=zeros(K,N);
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| 44 | for i = 1:Iterace,
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| 45 | %generovani stavu
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| 46 | % hold off
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| 47 | for n = 1:N,
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| 48 | Xkn(:, 1, n) = x0 + [sigma*randn(); 0; 0];
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| 49 | for k = 1:K-1,
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| 50 | Uk = uPi(k, Xkn(:, k, n));
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| 51 | % UU(k,n) = Uk;
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| 52 | Kk = Uk*Xkn(3, k, n)/(Uk^2*Xkn(3, k, n) + sigma^2);
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| 53 | Xkn(1, k+1, n) = Xkn(1, k, n) + Xkn(2, k, n)*Uk + sigma*randn();
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| 54 | Xkn(2, k+1, n) = Xkn(2, k, n) + Kk*(Xkn(1, k+1, n) - Xkn(1, k, n) - Xkn(2, k, n)*Uk);
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| 55 | Xkn(3, k+1, n) = (1 - Kk*Uk)*Xkn(3, k, n);
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| 56 | end
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| 57 | % hold all
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| 58 | % subplot(4,1,1);
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| 59 | % plot(1:K,Xkn(1,:,n))
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| 60 | % hold all
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| 61 | % subplot(4,1,2);
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| 62 | % plot(1:K,Xkn(2,:,n))
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| 63 | % hold all
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| 64 | % subplot(4,1,3);
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| 65 | % plot(1:K,Xkn(3,:,n))
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| 66 | % hold all
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| 67 | % subplot(4,1,4);
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| 68 | % plot(1:K,UU(:,n))
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| 69 |
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| 70 | end
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| 71 | Xstripe = mean(Xkn, 3);
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| 72 | % hold all
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| 73 | % subplot(4,1,1);
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| 74 | % plot(1:K,Xstripe(1,:),'-ro')
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| 75 | % hold all
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| 76 | % subplot(4,1,2);
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| 77 | % plot(1:K,Xstripe(2,:),'-ro')
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| 78 | % hold all
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| 79 | % subplot(4,1,3);
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| 80 | % plot(1:K,Xstripe(3,:),'-ro')
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| 81 |
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| 82 | %hold off
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| 83 | % Epsl = randn(3,N);
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| 84 | %iterace pro k = K-1..1
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| 85 | for k = K-1:-1:1,
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| 86 | gka = k;
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| 87 | % 1]
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| 88 | for n = 1:N,
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| 89 | %krive okoli
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| 90 | Xkn(1, k, n) = Xstripe(1, k) + rho*randn();
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| 91 | Xkn(2, k, n) = Xstripe(2, k) + rho*randn();
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| 92 | Xkn(3, k, n) = Xstripe(3, k)*rho*exp(randn());
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| 93 | % %rovne okoli
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| 94 | % Xkn(1, k, n) = Xstripe(1, k) + Epsl(1,n);
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| 95 | % Xkn(2, k, n) = Xstripe(2, k) + Epsl(2,n);
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| 96 | % Xkn(3, k, n) = Xstripe(3, k)*exp(Epsl(3,n));
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| 97 | end
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| 98 | % Xkn(:,k,:)
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| 99 |
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| 100 | % 2]
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| 101 | for n = 1:N,
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| 102 | gnu = n;
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| 103 | [Uopt(n), Hmin(n)] = fminunc(@Hamilt, uPi(k, Xkn(:, k, n)), optimset('GradObj','on','Display','notify'));
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| 104 | % [i, k, n]
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| 105 | %
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| 106 | % interv = -1000:1:1000;
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| 107 | % for ll = 1:2001,
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| 108 | % hodnot(ll) = Hamilt(interv(ll));
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| 109 | % end
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| 110 | % plot(interv, hodnot,'-b',Uopt(n),Hmin(n),'rs',uPi(k, Xkn(:, k, n)),Hamilt(uPi(k, Xkn(:, k, n))),'go')
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| 111 | % prah = 100;
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| 112 | % if(Uopt(n) > prah)
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| 113 | % Uopt(n) = prah;
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| 114 | % Hmin(n) = Hamilt(prah);
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| 115 | % disp('u > horni mez');
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| 116 | % elseif(Uopt(n) < -prah)
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| 117 | % Uopt(n) = -prah;
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| 118 | % Hmin(n) = Hamilt(-prah);
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| 119 | % disp('u < dolni mez');
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| 120 | % end
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| 121 | % if(extfl < 1)
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| 122 | % disp('exitflag < 1')
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| 123 | % end
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| 124 | end
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| 125 | % 3]
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| 126 | for n = 1:N, % V??? nema to byt k+1? ale asi ne
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| 127 | Vn(n) = Hmin(n) + Vtilde(k+1, Xkn(:, k, n));
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| 128 | % xxx(n) = Xkn(1,k,n);
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| 129 | % xxy(n) = Xkn(2,k,n);
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| 130 | % xxz(n) = Xkn(3,k,n);
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| 131 | % Vn(n) = xxx(n).*xxx(n).*xxx(n);
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| 132 | end
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| 133 | % xxx2 = sort(xxx);
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| 134 | % xxy2 = sort(xxy);
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| 135 | % xxz2 = sort(xxz);
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| 136 |
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| 137 | % 4]
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| 138 | Epsilon = zeros(3, N);
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| 139 | for n = 1:N,
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| 140 | Epsilon(:, n) = Xkn(:, k, n) - Xstripe(:, k);
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| 141 | end
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| 142 | mFi = matrixFi(Epsilon);
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| 143 | FiFiTInvFi = (mFi*mFi')\mFi;
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| 144 | Wv(:,k) = FiFiTInvFi * Vn';
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| 145 | % Wv = zeros(10,1);
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| 146 | % Wv(1, k) = Wvtmp(1);
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| 147 | % Wv(2, k) = Wvtmp(2);
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| 148 | % Wv(3, k) = Wvtmp(3);
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| 149 | % Wv(4, k) = Wvtmp(4);
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| 150 | % FiFiTInvFi = (mFi'*mFi)\mFi';
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| 151 | % Wv(:, k) = FiFiTInvFi' * Vn';
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| 152 | % UU(k,:) = Uopt;
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| 153 | for n = 1:N,
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| 154 | yt(n) = Xkn(1, k, n);
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| 155 | bt(n) = Xkn(2, k, n);
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| 156 | pt(n) = Xkn(3, k, n);
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| 157 | end
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| 158 | mPsi = [yt',...
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| 159 | bt'.*Uopt',...
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| 160 | pt'.*Uopt',...
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| 161 | Uopt'];
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| 162 | PsiPsiTInvPsi = (mPsi'*mPsi)\mPsi';
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| 163 | Kpi(:,k) = PsiPsiTInvPsi * (Rk(k)*ones(N,1));
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| 164 |
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| 165 | % for nn=1:N,
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| 166 | % vlv(nn) = Vtilde(k, [xxx2(nn);xxy2(nn);xxz2(nn)]);
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| 167 | % end
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| 168 | % subplot(3,1,1);
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| 169 | % plot(xxx,Vn,'rs',xxx2,vlv,'-b')
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| 170 | % subplot(3,1,2);
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| 171 | % plot(xxy,Vn,'rs',xxy2,vlv,'-b')
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| 172 | % subplot(3,1,3);
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| 173 | % plot(xxz,Vn,'rs',xxz2,vlv,'-b')
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| 174 | end
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| 175 | % clf reset
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| 176 | % for n=1:N,
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| 177 | %
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| 178 | % hold all
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| 179 | % subplot(4,1,1);
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| 180 | % plot(1:K,Xkn(1,:,n),'-b')
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| 181 | % hold all
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| 182 | % subplot(4,1,2);
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| 183 | % plot(1:K,Xkn(2,:,n),'-b')
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| 184 | % hold all
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| 185 | % subplot(4,1,3);
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| 186 | % plot(1:K,Xkn(3,:,n),'-b')
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| 187 | % hold all
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| 188 | % % subplot(4,1,4);
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| 189 | % % plot(1:K,UU(:,n),'-b')
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| 190 | % end
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| 191 | end
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| 192 | %%%%%%%%%%%
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| 193 | toc
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| 194 |
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| 195 | Kpi
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| 196 | %graficky vystup
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| 197 |
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| 198 | X = zeros(3, K);
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| 199 | UU = zeros(1,K);
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| 200 |
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| 201 | X(:,1) = x0 + [sigma*randn(); 0; 0];
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| 202 | for k = 1:K-1,
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| 203 | Upi = uPi(k, X);
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| 204 | UU(k) = Upi;
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| 205 | Ktmp = Upi*X(3,k)/(Upi^2*X(3,k) + sigma^2);
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| 206 | X(1,k+1) = X(1,k)+X(2,k)*Upi + sigma*randn();
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| 207 | X(2,k+1) = X(2,k) + Ktmp*(X(1,k+1) - X(1,k) - X(2,k)*Upi);
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| 208 | X(3,k+1) = X(3,k)*(1-Ktmp*Upi);
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| 209 | end
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| 210 | % X
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| 211 | % hold off
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| 212 | subplot(4,1,1);
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| 213 | plot(1:K,X(1,:),'-gs')
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| 214 | % hold off
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| 215 | subplot(4,1,2);
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| 216 | plot(1:K,X(2,:),'-gs')
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| 217 | % hold off
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| 218 | subplot(4,1,3);
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| 219 | plot(1:K,X(3,:),'-gs')
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| 220 | % hold off
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| 221 | subplot(4,1,4);
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| 222 | plot(1:K,UU,'-gs')
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| 223 | % X = zeros(1, K);
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| 224 | % b = 0;
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| 225 | % UU = zeros(1,K);
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| 226 | %
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| 227 | % X(1) = sigma*randn();
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| 228 | % for k = 1:K-1,
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| 229 | % Upi = uPi(k, [X,b,0]);
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| 230 | % UU(k) = Upi;
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| 231 | % X(k+1) = X(k) + b*Upi + sigma*randn();
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| 232 | % end
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| 233 | %
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| 234 | % % hold off
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| 235 | % subplot(2,1,1);
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| 236 | % plot(1:K,X,'-gs')
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| 237 | % % hold off
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| 238 | % subplot(2,1,2);
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| 239 | % plot(1:K,UU,'-gs')
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| 240 |
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| 241 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 242 | %pomocne funkce
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| 243 |
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| 244 | function [val_uPi] = uPi(k_uPi, x_uPi)
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| 245 | val_uPi = (Rk(k_uPi) - Kpi(1, k_uPi)*x_uPi(1))/(Kpi(2, k_uPi)*x_uPi(2) + Kpi(3, k_uPi)*x_uPi(3) + Kpi(4, k_uPi));
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| 246 | end
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| 247 |
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| 248 | function [val_ham, val_grad] = Hamilt(u_ham)
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| 249 | % Vtddx = Vtilde_dx(gka+1, Xkn(:, gka, gnu));
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| 250 | 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
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| 251 | + [Xkn(1, gka, gnu) + Xkn(2, gka, gnu)*u_ham; ...
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| 252 | Xkn(2, gka, gnu) + 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); ...
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| 253 | Xkn(3, gka, gnu) - Xkn(3, gka, gnu)^2*u_ham^2/(Xkn(3, gka, gnu)*u_ham^2 + sigma^2)]' ... %fce f
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| 254 | *Vtilde_dx(gka+1, Xkn(:, gka, gnu)) ...
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| 255 | + Wv(5, gka+1)*sigma;
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| 256 |
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| 257 | 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
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| 258 | + [Xkn(2, gka, gnu);...
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| 259 | (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));...
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| 260 | (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
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| 261 | * Vtilde_dx(gka+1, Xkn(:, gka, gnu)); %derivace Bellman fce
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| 262 | end
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| 263 |
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| 264 | function [val_Vt] = Vtilde(k_Vt, x_Vt)
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| 265 | if(k_Vt == K)
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| 266 | val_Vt = h;
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| 267 | else
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| 268 | val_Vt = vectFi(x_Vt - Xstripe(:, k_Vt))' * Wv(:,k_Vt);
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| 269 | end
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| 270 | end
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| 271 |
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| 272 | function [val_Vt] = Vtilde_dx(k_Vt, x_Vt)
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| 273 | if(k_Vt == K)
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| 274 | val_Vt = hdx;
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| 275 | else
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| 276 | val_Vt = difFi(x_Vt - Xstripe(:, k_Vt))' * Wv(:,k_Vt);
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| 277 | end
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| 278 | end
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| 279 |
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| 280 | % function [val_Vt] = Vtilde_dx_dx(k_Vt, x_Vt)
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| 281 | % if(k_Vt == K)
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| 282 | % val_Vt = hdxdx;
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| 283 | % else
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| 284 | % val_Vt = zeros(3,3);
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| 285 | % val_Vt(1,1) = 2*Wv(5,k_Vt);
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| 286 | % val_Vt(2,2) = 2*Wv(8,k_Vt);
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| 287 | % val_Vt(3,3) = 2*Wv(10,k_Vt);
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| 288 | %
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| 289 | % val_Vt(1,2) = Wv(6,k_Vt);
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| 290 | % val_Vt(1,3) = Wv(7,k_Vt);
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| 291 | % val_Vt(2,3) = Wv(9,k_Vt);
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| 292 | %
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| 293 | % val_Vt(2,1) = val_Vt(1,2);
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| 294 | % val_Vt(3,1) = val_Vt(1,3);
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| 295 | % val_Vt(3,2) = val_Vt(2,3);
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| 296 | % end
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| 297 | % end
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| 298 |
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| 299 | % function [val_Vt] = trSgVt(k_Vt)
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| 300 | % if(k_Vt == K)
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| 301 | % val_Vt = 0;
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| 302 | % else
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| 303 | % val_Vt = 2*Wv(5,k_Vt)*sigma;
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| 304 | % end
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| 305 | % end
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| 306 |
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| 307 | function [val_Fi] = vectFi(x_Fi)
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| 308 | val_Fi = [ ...
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| 309 | 1; ...
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| 310 | x_Fi(1); ...
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| 311 | x_Fi(2); ...
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| 312 | x_Fi(3); ...
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| 313 | x_Fi(1)^2; ...
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| 314 | x_Fi(1)*x_Fi(2); ...
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| 315 | x_Fi(1)*x_Fi(3); ...
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| 316 | x_Fi(2)^2; ...
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| 317 | x_Fi(2)*x_Fi(3); ...
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| 318 | x_Fi(3)^2; ...
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| 319 | ];
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| 320 | end
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| 321 |
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| 322 | function [val_Fi] = matrixFi(x_Fi)
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| 323 | val_Fi = [ ...
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| 324 | ones(1, N); ...
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| 325 | x_Fi(1, :); ...
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| 326 | x_Fi(2, :); ...
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| 327 | x_Fi(3, :); ...
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| 328 | x_Fi(1, :).^2; ...
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| 329 | x_Fi(1, :).*x_Fi(2, :); ...
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| 330 | x_Fi(1, :).*x_Fi(3, :); ...
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| 331 | x_Fi(2, :).^2; ...
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| 332 | x_Fi(2, :).*x_Fi(3, :); ...
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| 333 | x_Fi(3, :).^2; ...
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| 334 | ];
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| 335 | % val_Fi = [ ...
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| 336 | % ones(1, N); ...
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| 337 | % x_Fi(1, :); ...
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| 338 | % x_Fi(2, :); ...
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| 339 | % x_Fi(3, :); ...
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| 340 | % ];
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| 341 | end
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| 342 |
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| 343 | function [val_Fi] = difFi(x_Fi)
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| 344 | val_Fi = [ ...
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| 345 | 0 0 0; ...
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| 346 | 1 0 0; ...
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| 347 | 0 1 0; ...
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| 348 | 0 0 1; ...
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| 349 | 2*x_Fi(1) 0 0; ...
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| 350 | x_Fi(2) x_Fi(1) 0; ...
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| 351 | x_Fi(3) 0 x_Fi(1); ...
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| 352 | 0 2*x_Fi(2) 0; ...
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| 353 | 0 x_Fi(3) x_Fi(2); ...
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| 354 | 0 0 2*x_Fi(3); ...
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| 355 | ];
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| 356 | end
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| 357 | end |
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