Calaulation of Time-Optimal Control Law for Double Integrator System with Complex Constraints： Endpoint Backward Method

An endpoint backward method is proposed to calculate the time-optimal control law of double integrator system. First, the time intervals between the switch points and the endpoints are calculated. Then, the positions of switch points are decided according to the motion equation, and the switch line is formed. Theoretical analysis shows that this method can be used to solve the double integrator system with functional constraint target set and deal with the second order oscillation system.