The Spline Problem

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The Spline Problem

$\begin{array}{crclrcll} \displaystyle\min_{x,u} &\multicolumn{3}{l}{x_3(1)}\\ \text{unter} &\dot x_1(t) &=& x_2(t) \\ &\dot x_2(t) &=& u_1(t) \\ &\dot x_3(t) &=& u_1(t)^2 \\[.1cm] &x_1(0) &=& 0 &x_1(1) &=& 0 \\ &x_2(0) &=& 1 &x_2(1) &=& 1 \\ &x_3(0) &=& 0 \\[.1cm] &u_1(t)&\in&\multicolumn{5}{l}{[-6;6],\quad t\in[0;1]}\\ \end{array}$

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The Spline Problem