%% formulation
\documentclass{standalone}
\usepackage{amsmath}
\usepackage{bm}
\usepackage{graphicx}
\usepackage{xcolor}
\begin{document}
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\begin{align*}
\min_{t_f, \bm{u}(t)} \quad & t_f \\
\text{subject to:} \quad & \dot{\bm{x}} = \begin{bmatrix}
\frac{ \sin(x_3)[9/4\cos(x_3) x_1^2 + 2x_2^2 ] + 4/3 [u_1-u_2] - 3/2 \cos(x_3)u_2 }{31/36 + 9/4 \sin^2(x_3)} \\
\frac{ -[\sin(x_3)[7/2 x_1^2 + 9/4\cos(x_3) x_2^2] - 7/3u_2 + 3/2 \cos(x_3) [u_1 - u_2] ]    }{31/36 + 9/4 \sin^2(x_3)} \\
x_2 - x_1 \\
x_1
\end{bmatrix} \\
& \bm{x}(0) = (0,0,0.5,0) \\
& \bm{x}(t_f) = (0,0,0.5,0.522) \\
& \bm{0} \leq \bm{x} \\
& -1 \leq u_1 \leq 1 \\
& -1 \leq u_2 \leq 1
\end{align*}
}}
\end{document}

%% solution