%% computeTrustRegionExploitation
% computes a scalar measure for the
% exploitation of the trust region.
%
%% Syntax
%
% <html>
%        <div class="syntax">
% trExploitation = computeTrustRegionExploitation(obj,var_s,termRegSet) <br>
%        </div>
% </html>
%
%% Description
% This function computes the smallest value of the auxiliary variable
% tau_0 in the constraint in [1, Eq. 28a], which is considered a
% scalar measure for the exploitation of the trust region. It holds
% that
% zonotope(termReg.c,termReg.G*diag(var_s)) \subseteq
% termReg + trExploitation*tr_set,
% i.e., 0 <= trExploitation <= 1 for any feasible var_s.
% We require (a feasible value of) tau_0 to evaluate the
% parameterized approximation of the abstraction error.
%
%% 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
%            (array of dimension [size(termReg.G,2),1])
%        </p>
%    </td>
%    </tr>
%    <tr bgcolor="#F2F2F2">
%    <td>
%        <p class="table">
%            termReg
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            current candidate for the terminal region
%            (class: zonotope)
%        </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">
%            trExploitation
%        </p>
%    </td>
%    <td>
%        <p class="table">
%            scalar between 0 and 1
%        </p>
%    </td>
%    </tr>
% </tbody>
% </table>
% </html>
%
%% See Also
% <matlab:doc('@computeTermRegNonlinSysLinApproach/approxAbsErrQuad_eval') @computeTermRegNonlinSysLinApproach/approxAbsErrQuad_eval>
%
%% 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>
