Time-optimal control by iterative dynamic-programming

Although it is possible to have singular subarcs in time-optimal control, in most of the time interval the control is bang-bang in nature. We therefore apply iterative dynamic programming to search simultaneously for the switching times and for the values for control. Instead of using stages of equal length, we use stages of varying length so that switching times can be accurately determined. Computations based on three examples show that the optimal control policy can be obtained without difficulty even when the system equations are highly nonlinear. The computational procedure is straightforward, and the computations can be readily carried out on a personal computer.