Synthesis of a control in the problem of the time-optimal transfer of a point mass to a specified position with zero velocity (Q2714645)

The authors study the time-optimal control of the motion of a material point of constant mass under the action of a bounded force. The control is modelled by the equations NEWLINE\[NEWLINE \begin{gathered} \dot x = v,\quad \dot v = u,\quad x(0) = x^0,\quad v(0) = v^0,\\ x(t_f) = 0,\quad v(t_f) = 0,\quad t_f\to \min\limits_u,\quad \|u\|\leq 1. \end{gathered}\tag{1} NEWLINE\]NEWLINE A control algorithm and a Bellman function are constructed. Results of numerical investigation for various initial values of velocity are presented.