one additional control input. The augmented states have the following system dynamics $$\begin{aligned}
& 1': \left\{ \begin{array}{ll}
        \dot{x}_3 = -x_3 + 2 x_3 u_2 \\
        \dot{x}_4 = x_4 + x_4 u_2
        \end{array} 
\right.,   \quad
2': \left\{ \begin{array}{ll}
        \dot{x}_3 = x_3 - 3 x_3 u_2 \\
        \dot{x}_4 = 2 x_4 - 2 x_4 u_2
        \end{array} 
\right.   \notag \\
& 3': \left\{ \begin{array}{ll}
        \dot{x}_3 = 2 x_3 + x_3 u_2 \\
        \dot{x}_4 = -x_4 + 3 x_4 u_2
        \end{array} 
\right.\end{aligned}$$ with the initial condition $\vx_0 = \begin{bmatrix} 2, 3, 1, 1 \end{bmatrix}^{\top}$. The cost function is the same as Example 1 with $\vx_g = \begin{bmatrix} 1, -1, 2, 2\end{bmatrix} ^{\top}$. As Example 1, the optimized solutions are comparable for both algorithms (refer to Table \[tab:performance\]). However the CPU times are drastically different. For the BVP method, the CPU time is about 1500 seconds while the OCS2 algorithm uses only 76 seconds which is 19.5 times more efficient. This manifests the efficiency of the OCS2 algorithm in higher dimensional problems where computational time of the BVP algorithm prohibitively increases.

![Comparison between the CPU time consumption of the BVP algorithm (blue) and the OCS2 algorithm (orange). The evaluation is done on an Intel’s core 