%% formulation
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\begin{align*}
\min_{u(t)} \quad & S(x(t_f) - \eta)^2 + \int_{t_0}^{t_f}\left[ \frac{1}{\epsilon_m^2}(x(t) - \eta)^2 + \frac{1}{u_m^2} u^2(t) \right] \mathrm{d}t \\
\text{subject to:} \quad & \dot{x}(t) = -\frac{1}{a}x(t) + u(t) \\
& x(0) = x_0 \\
\text{where:} \quad & \eta \text{ is a constant}
\end{align*}
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%% solution