时间最优开关控制的非线性规划方法

提出单输入非线性时间最优开关控制的非线性规划算法．针对不同的开关控制划分未知时间段，以时间段为变量建立与最优控制等价的非线性规划模型．构造每个未知时间段的等分龙格库塔格式，该格式不但不增加未知变量，而且可构造出不含导数的非线性规划算法．利用龙格库塔格式的收敛性和非线性规划的一阶最优性条件证明该方法的收敛性．最后以实例验证该算法．

Nonlinear programming method for time optimal switching control

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.