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Mo, Yilin added begin_algorithm_caption_Identification_algorithm__.tex
over 8 years ago
Commit id: 43c8fbf276a9c4a4b33f8754581b184091c2de3b
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\begin{algorithm}
\caption{Identification algorithm for $\mG(z)$, $\mK(z)$}
\textbf{Inputs:} Input-output data $y_k$ and $u_k$.\\
\textbf{Outputs:} The transfer functions $\mG$ and $\mK$.
\begin{step}
Compute $\Phi_{y,u}(z)$ from input-output data $y_k$ and $u_k$ and let $\Psi_{y,u}(s)=\Phi_{y,u}(\frac{1+s}{1-s})$;
\end{step}
\begin{step}
Each element in $\Psi[i,j](s)$ can be expanded as a sum of partial fractions and a term $\Psi[i,j](\infty)$. Those partial fractions with poles in $Re[s] < 0$ may then be summed together, and when add to $\frac{1}{2}\Psi[i,j](\infty)$ yield $\mS[i,j](s)$;
\end{step}
\begin{step}
Compute $\mW(s)$ from \eqref{eq:and} for a minimal realization of $\mS(s)$ and a properly chosen $R\succeq0$.
\end{step}
\begin{step}
Compute $\hat{D}_{22}$ based on $\mW\left(\frac{z-1}{z+1}\right)$ from \eqref{eq:D22}.
\end{step}
\begin{step}
Once an estimate $\hat{\mC}(z)$ is computed using \eqref{eq:estC} and we can obtain $\mG(z)$ and $\mK(z)$ using \eqref{eq:khg}.
\end{step}
\label{alg:main}
\end{algorithm}
