%% formulation
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\begin{align*}
\min_{u,\bm{\xi},\bm{p}} \quad & \int_{0}^{t_f} \left[ w_1 \xi_1^2 + w_2 \dot{\xi}_4^2 + w_3 u^2 \right] dt \\
\text{subject to:} \quad & \dot{\bm{\xi}}(t) =
\begin{bmatrix} 0 & 1 & 0 & 0 \\\frac{-k_t}{m_{us/4}} & \frac{-[K_s(x_p) + c_t]}{m_{us/4}}& \frac{c_s(x_p)}{m_{us/4}}& \frac{k_s(x_p)}{m_{us/4}} \\ 0 & -1 & 0 & 1 \\ 0 & \frac{k_s(x_p)}{m_{s/4}} & \frac{-c_s(x_p)}{m_{s/4}}& \frac{-k_s(x_p)}{m_{s/4}}
\end{bmatrix} \bm{\xi}(t) +
\begin{bmatrix}
0 \\ \frac{-1}{m_{us/4}} \\0 \\ \frac{1}{m_{s/4}}
\end{bmatrix}u(t) +
\begin{bmatrix}
-1 \\ \frac{c_t}{m_{us/4}} \\ 0 \\ 0
\end{bmatrix}\dot{z}_0(t) \\
& \bm{\xi}(0) = \bm{0} \\
&\bm{G}_o(x_p) \leq \bm{0} \\
&\bm{G}_i(x_p,\xi(t)) \leq  \bm{0} \\
& \bm{p}_{\min} \leq \bm{p} \leq \bm{p}_{\max}
\end{align*}
}}
\end{document}

%% solution