%% formulation
\documentclass{standalone}
\usepackage{amsmath}
\usepackage{bm}
\usepackage{graphicx}
\usepackage{xcolor}
\begin{document}
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\begin{align*}
\min_{u(t)} \quad & x_1(t_f) \\
\text{subject to:} \quad & \dot{\bm{x}} = \begin{bmatrix}
- \zeta x_1 \log(x_1/x_2) \\
x_2 \left( b - \mu - d x_1^{2/3} + G u \right)
\end{bmatrix} \\
& \bm{x}(0) = \bm{x}_0 \\
& 0 \leq u(t) \leq u_{\max} \\
& \int_0^{t_f} u(t) \mathrm{d}t \leq A
\end{align*}
}}
\end{document}

%% solution