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04/28/10 00:16:27 (15 years ago)
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zimamiro
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  • applications/dual/SIDP/text/ch2.tex

    r917 r918  
    4444 
    4545O��nou ztr� nyn�� ps�ve tvaru 
    46 \begin{equation} 
    47 J_N(I_N)=\tilde{g}_N(I_N) 
    48 \end{equation} 
    49 \begin{equation} 
     46\begin{gather} 
     47J_N(I_N)=\tilde{g}_N(I_N)\\ 
    5048J_t(I_t)=\min_{u_t \in U_t}\E_{w_t,y_{t+1}}\left\{\tilde{g}_t(I_t,u_t,w_t)+J_{t+1}((I_t,u_t,y_{t+1}))|I_t,u_t\right\} \qquad t=0,\ldots,N-1 
    51 \end{equation} 
     49\end{gather} 
    5250 
    5351Tato � ji� m��ena pomoc�ynamick� programov�. P��en�udeme postupovat od konce �� horizontu a postupn�ledat $J_t(I_t)$. Potom libovoln�\pi=\{\mu_0,\ldots,\mu_{N-1}\}$, kter�ab�nim����n�tr� $J_0(y_0)$ je optim��osloupnost rozhodnut� 
    … …  
    159157P_{t+1}=(I-K_tA_t)P_t 
    160158\end{equation} 
    161 Celkov�edy od p�� odhadu parametru $N(\hat{\theta}_t,P_t)$ k nov� $N(\hat{\theta}_{t+1},P_{t+1})$ p�me pomoc�\begin{equation} 
    162 K_t=P_tA_t(A_t^TP_tA_t+Q_t)^{-1} 
    163 \end{equation} 
    164 \begin{equation} 
    165 \hat{\theta}_{t+1}=\hat{\theta}_t+K_t(x_{t+1}-f_t(x_t,u_t)-A_t\hat{\theta}_t) 
    166 \end{equation} 
    167 \begin{equation} 
    168 P_{t+1}=(I-K_tA_t)P_t 
    169 \end{equation} 
     159Celkov�edy od p�� odhadu parametru $N(\hat{\theta}_t,P_t)$ k nov� $N(\hat{\theta}_{t+1},P_{t+1})$ p�me pomoc�\begin{gather} 
     160K_t=P_tA_t(A_t^TP_tA_t+Q_t)^{-1}\\ 
     161\hat{\theta}_{t+1}=\hat{\theta}_t+K_t(y_{t+1}-\tilde{h}_t(I_t,u_t)-A_t\hat{\theta}_t),\\ 
     162P_{t+1}=(I-K_tA_t)P_t. 
     163\end{gather} 
    170164 
    171165Tato odhadovac�rocedura se naz�lman�ltr [ref].