Changeset 1090 for applications/dual/SIDP/text/ch4.tex

Timestamp:

06/13/10 17:27:15 (14 years ago)

Author:

zimamiro

Message:

 

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• applications/dual/SIDP/text/ch4.tex (modified) (5 diffs)

applications/dual/SIDP/text/ch4.tex

@@ -1 @@
-V t� kapitole je pops�jednoduch�� na kter�jsou porovn� ��lgoritmy uveden� p�l�apitole. Syst�byl podrobn�koum�v \cite{astrom1986dual}. Pro srovn� uv�me tam���y.
+V t� kapitole je pops�jednoduch��zkouman�ite{astrom1986dual}. Na n�jsou porovn� ��lgoritmy uveden� p�l�apitole.
 
 \section{Popis syst�}
@@ -5 +5 @@
 \begin{gather}
 \label{simple}
-y_{t+1}=y_t+\theta_tu_t+v_{t+1} \qquad t=0,\ldots,N-1,\\
-v_t\sim N(0,\sigma^2).\\
-\theta_t\sim N(\hat{\theta},P_t),\\
+y_{t+1}=y_t+\theta u_t+v_{t+1}  \qquad t=0,\ldots,N-1,\\
+v_{t+1}\sim N(0,\sigma^2),
+\end{gather}
+kde rozptyl �umu $\sigma$ je zn�
+
+O nezn�m parametru $\theta$ m� v �e $t$ informaci v podob�ostate� statistiky $T_t=(\hat{\theta},P_t)$, tvo�st� hodnotou a rozptylem. P�kl�me nekorelovanost $\theta$ s �umem, tedy �e
+\begin{equation}
 \cov(v_{t+1},\theta)=0.
-\end{gather}
+\end{equation}
 
 Ztr�vou funkci vol� kvadratickou, tedy
 \begin{equation}
-g(y_{0:N},u_{0:N-1},v_{0:N-1})=\sum_{t=0}^{N-1}y_{t+1}^2.
+g(y_{0:N},u_{0:N-1})=\sum_{t=0}^{N-1}y_{t+1}^2.
 \end{equation}
 
@@ -24 +28 @@
 \end{gather}
 
-O��n�tr� je
+Hyperstav syst� $H_t$ tvo�ktor $(y_t,\hat{\theta}_t,P_t)$. O��n�tr� je
 \begin{equation}
-J_t(y_t,\theta_t)=\min_{u_t \in U_t}\E_{y_{t+1},v_t}\left\{y_{t+1}^2+J_{t+1}(y_{t+1},\theta_{t+1})|y_t,\theta_t,u_t\right\}, \qquad t=0,\ldots,N-1.
+J_t(H_t)=\min_{u_t \in U_t}\E_{y_{t+1},v_t}\left\{y_{t+1}^2+J_{t+1}(H_{t+1})|H_t,u_t\right\}, \qquad t=0,\ldots,N-1.
 \end{equation}
 
@@ -35 +39 @@
 \end{gather}
 
-ZDE BY MEL BYT ANGSTROM+...
-
 \section{Specifika jednotliv��up� tomto odd� jsou pops� n�er�spekty algoritm�er�udeme srovn�t, p�likaci na syst�\eqref{simple}.
 
@@ -42 +44 @@
 O��n�tr� \eqref{CE} prejde v
 \begin{gather}
-J_t(y_t, \theta_t)=\min_{u_t \in U_t}\left\{\hat{y}_{t+1}^2 +J_{t+1}(y_{t+1},\theta_{t+1})|I_t,\theta_t,u_t\right\}.
+J_t(H_t)=\min_{u_t \in U_t}\left\{\hat{y}_t^2 +J_{t+1}(\hat{H}_{t+1})|I_t,\theta_t,u_t\right\}.
 \end{gather}
 St� hodnota v� je