\section{Experimental results}\label{experiment}\vspace{1ex}%\noindent
The  stochastic tracker described in Section~\ref{detection} was
simulated. While simulating, we specify the two phases named
``before'' and ``after'' (before and after a parameter change).
The phase ``before'' takes 300 time instants and phase ``after''
takes 3000 time instants. In totality, simulation parameters
comprise:
\begin{enumerate}
\item Number of Iterations \dotfill 3000
\item Number of Samples  to average results, $L$ \dotfill 20
\item Sample size, $M$ \dotfill 150
\item Numerical algorithms and their parameters:
   \begin{enumerate}
     \item Robbins-Monroe procedure \dotfill SSA
     \item Simplified Least Squares \dotfill SLS
     \item Exponential smoothing parameter, $\alpha$ \dotfill 0.5   \end{enumerate}
\item Simulated genetic algorithm:
   \begin{enumerate}
     \item Chromosome Length (bits) \dotfill 7
     \item Power (size) of population, $K$ \dotfill 50
     \item Elite Factor \dotfill 2
     \item Mutation Probability Rate \dotfill 0.100
     \item Selection Mode \dotfill Remainder stochastic sampling
     \item Crossover Mode \dotfill Two-point crossover
   \end{enumerate}
\end{enumerate}

\begin{center}
\begin{figure}%[h]
\centering
\includegraphics[scale=1]{GA-1.eps}
\caption{Genetic algorithm performance:
$\hat K_{\mathrm{p}}$ and $\hat K_{\mathrm{r}}$.}
\label{GA-1-PRM}
\end{figure}
\end{center}


\begin{center}
\begin{figure}%[h]
\centering
\includegraphics[scale=1]{GA-2.eps}
\caption{Genetic algorithm performance: $\hat K_{\mathrm{p}}$.}
\label{GA-1-P}
\end{figure}
\end{center}


\begin{center}
\begin{figure}%[h]
\centering
\includegraphics[scale=1]{IPE-CP.eps}
\caption{Integral Percent Error for the controlled plant.
Comparison of three methods: SSA, SLS, GA.}
\label{IPE-P}
\end{figure}
\end{center}


\begin{center}
\begin{figure}%[h]
\centering
\includegraphics[scale=1]{IPE-RM.eps}
\caption{Integral Percent Error for the reference signal model.
Comparison of  SSA, SLS and GA.}
\label{IPE-RM}
\end{figure}
\end{center}
%***************************************************************

\vspace{-3.4cm}

Figures  \ref{GA-1-PRM} to  \ref{IPE-RM} demonstrate the
experimentally observed results  averaged over 100 program
runs for the following tasks: \\[-1.8ex]

(1) Determine the convergence  of GA-estimates
$\hat K_{\mathrm{p}}$ and $\hat K_{\mathrm{r}}$ for the
plant and reference model (Fig.~\ref{GA-1-PRM}).\\[-1.5ex]

(2) The same but in more detail for $\hat K_{\mathrm{p}}$
(Fig.~\ref{GA-1-P}).\\[-1.7ex]

(3) Compare the cumulative integral percent error  for
the plant between SSA, SLS and GA (Fig.~\ref{IPE-P}).\\[-1.8ex]

(4) The same but for the reference model
(Fig.~\ref{IPE-RM}).\\[-1ex]

\noindent
As revealed by the graphs for the controlled plant,
the settling time defined as the time required for the
estimates to settle within the band of $\pm 7 \%$ error,
ranges up to 750 time instants, i.e., 5 samples of $M=150$
readings needed  to make a decision on updating the filter
population. In another way, it has taken only 5 generations
of  $\mathscr{FP}$ for the error to  enter the band. However,
another experiments show that this quantity may increase
from 5 to 15.

According to simulation studies, GAs appear better capable for the
closed loop, than for the open-loop, control systems re-design.
Probably, this is due to the generic advantage of feedback systems
to decrease the sensitivity of the system to parameter
disturbances within the system.
%***************************************************************
