%% formulation
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\begin{document}
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\begin{align*}
\min_{u(t)} \quad & m\left[ x(t_f) \right]^2 + \int_0^{t_f} r u^2 \mathrm{d}t \\
\text{subject to:} \quad & \dot{x} = b u + a_1 \sin(\omega_1 t) + a_2 \sin(\omega_2 t) \\
& x(0) = x_0
\end{align*}
}}
\end{document}

%% solution