1. Consider the CFTOC
\begin{align*}
\min_{X_0, U_0} & u_0^2 + u_1^2 + u_2^2 + u_3^2 + x_0^2 + x_1^2 + x_2^2 + x_3^2 + x_4^2 \\
subject\ to & x_{k+1} = x_k + u_k, \quad k = 0, 1, 2, 3 \\
& x_0 = x(0)
\end{align*}
where $x_k \in \mathbb{R}$, $u_k \in \mathbb{R}$, $X_0 = [x_0, x_1, x_2, x_3, x_4]^T \in \mathbb{R}^5$, $U_0 = [u_0, u_1, u_2, u_3]^T \in \mathbb{R}^4$.
1. Use the Batch approach with shrinking horizon to compute $F_2^B$ (i.e. $u_2^* = F_2 x_2$).
2. Use Dynamic Programming to compute $F_2^{DP}$ (i.e. $u_2^* = F_2 x_2$).
3. Use Infinite-Horizon LQR to compute $F_2^{LQR, inf}$ (i.e. $u_2^* = F_2 x_2$).
