Analytical synthesis of time-optimal control in a third-order system (Q2761314)

The paper deals with the time-optimal control of a third-order system \(\dddot x = u\), \(x(0) = x^0\), \(\dot x(0) = \dot x^0\), \(\ddot x(0) = \ddot x^0\), \(x(t_f) = \dot x(t_f) = \ddot x(t_f) = 0\), \(t_f\to \min_u\), \(u^-\leq u\leq u^+\), \(u^-<0\), \(u^+>0\). This system describes the dynamics of material point subjected to a regulable force. The authors construct an optimal control with respect to the feedback (synthesis), and in the form of open-loop (program). Finally, the authors investigate the influence of asymmetry of constraints.