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Update problem_formulation_ocp_mex.tex with J_sbx^e #954

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Aug 10, 2023
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Update problem_formulation_ocp_mex.tex with J_sbx^e #954

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4 changes: 2 additions & 2 deletions docs/problem_formulation/problem_formulation_ocp_mex.tex
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Expand Up @@ -120,13 +120,13 @@ \section{Problem Formulation}\label{sec:problem}
%% lower terminal constraints
&&&\mathComment{Terminal constraints with lower bounds, see section \ref{sec:constraints:terminal}}\nonumber\\
&&&\underline{h}\terminal \leq h\terminal(x(T), p) + J\ind{sh}\terminal\, s\lowerh\terminal, &&\label{eq:constraints:terminal:lower_bounds:start}\\
&&&\underline{x}\terminal \leq J_{\textrm{bx}}\terminal\, x(T) + J\ind{sbx}\, s\lowerbx\terminal, &&\\ % TODO: add Jsbx_e?!
&&&\underline{x}\terminal \leq J_{\textrm{bx}}\terminal\, x(T) + J\ind{sbx}\terminal\, s\lowerbx\terminal, &&\\ % TODO: add Jsbx_e?!
&&&\underline{g}\terminal \leq C\terminal\, x(T) + J\ind{sg}\terminal\, s\lowerg\terminal \leq \bar{g}\terminal, && \\
&&& s\lowerh\terminal, s\lowerbx\terminal, s\lowerbu\terminal, s\lowerg\terminal \geq 0, \label{eq:constraints:terminal:lower_bounds:end}\\[1ex]
%% upper terminal constraints
&&&\mathComment{Terminal constraints with upper bound, see section \ref{sec:constraints:terminal}}\nonumber\\
&&& h\terminal(x(T), p) - J\ind{sh}\terminal\, s\ind{u,h}\terminal \leq \bar{h}\terminal, &&\label{eq:constraints:terminal:upper_bounds:start}\\
&&& J_{\textrm{bx}}\terminal\, x(T) - J\ind{sbx}\, s\ind{u,bx}\terminal \leq \bar{x}^{e}, &&\\ % TODO: add Jsbx_e?!
&&& J_{\textrm{bx}}\terminal\, x(T) - J\ind{sbx}\terminal\, s\ind{u,bx}\terminal \leq \bar{x}^{e}, &&\\ % TODO: add Jsbx_e?!
&&& C\terminal\, x(T) - J\ind{sg}\terminal\, s\ind{u,g}\terminal \leq \bar{g}\terminal \\
&&& s\upperh\terminal, s\upperbx\terminal, s\upperbu\terminal, s\upperg\terminal \geq 0,\label{eq:constraints:terminal:upper_bounds:end}
\end{align}
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