Abstract: A nonlinear programming method for time optimal switching control with a single control input is proposed. The unknown arc time is partitioned off the unknown durations of the segmental times in different switching control problems, and the nonlinear programming model equivalent to the optimal control is constituted with the time segments serving as variables. The Runge-Kutta numerical formulations based on average partitioning of each time segment are formed, which do not increase the number of the unknown variables but constitute a nonlinear programming without the derivative of all the functions. The convergence of the method is derived from the convergence of the Runge-Kutta formulations and the first-order necessary optimality condition. Finally, the proposed method is applied to some examples to demonstrate the effectiveness of the method.

Key words: time optimal control, switching control, nonlinear programming, Runge-Kutta method