Sme help with Identification?!

FaroukSchw

Hello guys, i am trying to identify the following non linear parameter varying system.
\begin{equation}
Y_1(t_{i})}=\frac{Y_1(t_{i-1})+\Delta t.k_{1}.Y_2(t_{i-1})}{\left(1+\Delta.t.\left(k_{1}.Y_2(t_{i-1})+k_{2}.Y_3(t_{i-1})\right)\right)}
\end{equation}

\begin{equation}
Y_2(t_{i})=\frac{U_1(t_{i})}{\left1+\frac{M_1}{U_4(t_{i})}(a\lefta.\fra c{1}{2}.k_{1}.Y_1(t_{i})+b.\frac{1}{2}.k_{4}.Y_3(t_{i-1})\right)\right}
\end{equation}

\begin{equation}
Y_3(t_{i})=\frac{U_2(t_{i})}{\left1+\frac{M_2}{U_4(t_{i})}(\left a.k_{2}.Y_1(t_{i})+b.k_{4}.Y_2(t_{i})\right)\right}
\end{equation}

\begin{equation}
Y_4(t_{i})=U_3+\frac{M_3}{M_2}\left(U_2(t_{i})-Y_3(t_{i})\right)
\end{equation}

Does any body has an idea about the algorithm that can be used?
Regards

FaroukSchw

It seems that i din't write with .tex well, here is a pdf containing the model.

Attached Files

LaTeX2.pdf (74.3 KB, 2 views)