Abstract: To solve optimal control problem,the control vector parameterization(CVP)approach is often used and the time grid nodes are usually fixed.In each time intervals,the controls are approximated by a function of time,which is determined by parameters.The partition of time grid will take effects on the accuracy and performance of the numerical optimization algorithm used to solve the original optimal control problem.A CVP method with variable time nodes is presented to optimize both of the control parameters and time nodes in the grid partition.The time node parameter is introduced by sigmoid function which approximate the switch procedure in the piecewise constant parameterization method.The derivatives of the performance to time nodes are derived and the time nodes constraints are handled by a given algorithm.An example of optimal control problem with two controls is solved by the proposed method.The different time grid partitions of two controls are obtained which show a higher approximation of the optimal control trajectories.

Key words: optimal control, control vector parameterization, time nodes

摘要： 控制向量参数化方法是求解最优控制的一种常用方法,其时间网格通常是固定的。在每个时间段上,控制向量表示为由一组参数确定的时间的函数。时间网格的划分会影响到数值求解最优控制问题时最优化算法的准确性和效率。为了同时优化控制参数和时间网格的节点,提出了一种可变时间节点控制向量参数化方法,通过带有时间参数的S型函数来近似分段常数参数化方法中的切换过程。推导出了最优控制性能指标对时间参数的导数,并提出了处理时间节点约束的算法。利用所提出方法求解带有两个控制的最优控制实例,对于两个控制获得了不同的时间网格划分,从而能够更好地近似最优控制轨迹。

关键词: 最优控制, 控制向量参数化, 时间节点