%% formulation
\documentclass{standalone}
\usepackage{amsmath}
\usepackage{bm}
\usepackage{graphicx}
\usepackage{xcolor}
\begin{document}
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\begin{align*}
\min_{u(t)} \quad & -x_2(t_f) \\
\text{subject to:} \quad & \dot{\bm{x}} = \begin{bmatrix}
- u x_1 \\ u x_1 - \rho u^k x_2
\end{bmatrix} \\
& -0.1 \leq x_1(t) \leq 1.1 \\
& -0.1 \leq x_2(t) \leq 1.1 \\
& a_L \leq u(t) \leq a_U \\
& \bm{x}(0) = (1,0.01)
\end{align*}
}}
\end{document}

%% solution