%% cvx_paramReachSet
% computes the parameterized approximation of the
% time-point reachable set.
%
%% Syntax
%
% <html>
%        <div class="syntax">
% [c_Rparam,G_Rparam] = cvx_paramReachSet(obj,var_s,var_Gctrl,var_RabsEerr,Rfexp,AB_d,RlinW,termRegSet) <br>
%        </div>
% </html>
%
%% Description
% This function computes the center and generator matrix of the
% zonotope representing the parameterized time-point reachable set as
% described in [1, Eq. 19a and Eq. 20].
%
%% 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">
%            obj
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            instance of class
%            computeTermRegNonlinSysLinApproach
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            var_s
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            generator scaling factors
%            (positive double vector of dimension;
%            [obj.termRegOrder*obj.nx,1])
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            var_Gctrl
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            generator matrix of zonotopic representation of the
%            invariance-preserving control law
%            (double matrix of dimension;
%            [obj.nu,obj.termRegOrder*obj.nx])
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            var_RabsEerr
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            reachable set due to set of abstraction errors
%            (struct with the fields:;
%            .c: center of var_Rerr;
%            (double vector of length nx);
%            .G: generator matrix of var_Rerr;
%            (double matrix);
%            )
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            Rfexp
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            reachable set of the linearized system due to the
%            constant input "dynamics evaluted at expansion
%            point"
%            (class: zonotope)
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            AB_d
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            horizontal concatenation of system matrix and input
%            matrix of the linearized system dynamics
%            (class: matZonotope)
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            RlinW
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            reachable set of the linearized dynamics due to the
%            disturbances
%            (class: zonotope)
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            termRegSet
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            current candidate for the the terminal region
%            (class: zonotope)
%        </p>
%    </td>
%    </tr>
% </tbody>
% </table>
% </html>
%
%% Output Argument
%
% <html>
% <table cellspacing="0" cellpadding="4" width="" border="1" frame="box" rules="none" class="">
% <tbody valign="top">
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            c_Rparam
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            center of the parameterized reachable set at the
%            next time step
%            (double array of dimension [nx,1])
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            G_Rparam
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            generator matrix of the parameterized reachable set
%            at the next time step
%            (double array)
%        </p>
%    </td>
%    </tr>
% </tbody>
% </table>
% </html>
%
%% See Also
% <matlab:doc('-') ->
%
%% References
% [1] L. Schäfer et al. "Scalable Computation of Robust Control
% Invariant Sets of Nonlinear Systems", in IEEE Transactions
% on Automatic Control, vol. 69, no. 2, pp. 755-770, 2024
%

%%
% <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>
%   <td style="background-color:#ffffff; border:0; width:25%; vertical-align:middle; text-align:center">
%             <img src="img/logoAroc.png" alt="logoAroc" height="40px">
%      </td>
%   <td style="background-color:#ffffff; border:0; width:25%; vertical-align:middle; text-align:center">
%      <img src="img/logoCora.png" alt="logoCora" height="40px"></td>
%   <td style="background-color:#ffffff; border:0; width:25%; vertical-align:middle; text-align:center">
%      <img src="img/logoChair.png" alt="logoChair" height="40px"></td>
%   <td style="background-color:#ffffff; border:0; width:25%; vertical-align:middle; text-align:center">
%      <img src="img/logoTum.png" alt="logoTum" height="40px"></td>
%  </tr>
% </table>
% </div>
% </html>
