Minimum time control of a second-order system

A new algorithm for determining the switching time and final time for the minimum-time control of a second-order system is described. We show that if there is only one switch in the bang-bang control, then the switching time and final time are related through an affine mapping. This mapping is determined by the system dynamics, the initial and target states, and the control bounds on the control input. The resulting time-optimal controller is easy to design and implement, making it suitable for online implementation. Since the algorithm also produces the final time, it becomes feasible to optimize the switching sequence over a collection of states to be visited so as to minimize the total visiting time.