%% scaleInitialSet
% scale the initial set so the goal set is reached
%
%% Syntax
%
% <html>
%        <div class="syntax">
% [R0opt,RcontOpt] = scaleInitialSet(sys,R0,H,goalSet,U,iter,Opts) <br>
%        </div>
% </html>
%
%% Description
% This function scales the initial set for reachability analysis in
% such a way that the final reachable set is located inside the goal
% set.
%
%% Input Arguments
%
%
% <html>
% <table cellspacing="0" cellpadding="4" width="" border="1" frame="box" rules="none" class="">
% <tbody valign="top">
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            sys
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            object that represents the dynamics of the closed-loop
%            system (class: nonlinParamSys)
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            R0
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            initial set (class: zonotope)
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            H
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            matrix storing the generator-to-input assignment
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            goalSet
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            goal set that should be reached (class: zonotope)
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            U
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            cell-array containing the sets of admissble control
%            inputs for all intermediate time steps
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            iter
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            index of the current time step
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            Opts
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            structure containing the following options
%        </p>
%        <p class="table">
% <table cellspacing="0" cellpadding="4" width="" border="1" frame="box" rules="none" class="inner">
% <tbody valign="top">
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            .iter
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            number of iterations for optimization
%        </p>
%    </td>
%    </tr>
% </tbody>
% </table>
%        </p>
%    </td>
%    </tr>
% </tbody>
% </table>
% </html>
%
%% Output Arguments
%
%
% <html>
% <table cellspacing="0" cellpadding="4" width="" border="1" frame="box" rules="none" class="">
% <tbody valign="top">
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            R0opt
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            scaled initial set (class: zonotope)
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            RcontOpt
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            cell-array storing the time interval reachable set for
%            the final solution
%        </p>
%    </td>
%    </tr>
% </tbody>
% </table>
% </html>
%
%% See Also
% <safetyNetControlhelp.html |safetyNetControl|>
%

%%
% <html>
%   <hr>
%   <p class="copy">&copy; 2018-2026 I6 Technische Universit&auml;t M&uuml;nchen
%        <tt class="minicdot">&#149;</tt>
%        <a href="https://tumcps.github.io/AROC/">Website</a>
%        <tt class="minicdot">&#149;</tt>
%        <a href="file:txts/LICENSE.txt">License</a>
%   </p>
% <div>
% <table>
%  <tr>
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