轨綫两端均受限制时的最优控制问題

本文用文献4]中的方法,首先处理了轨线两端均受限制时的快速最优控制问题,得到控制最优性的必要条件以及在某种意义下的充分条件;还得到有关微分方程的边界条件,并说明其几何意义,即贯截条件.此外,又讨论了所用方法中乘子的性质及作用. 对于一般意义下的以及文献4]中所讨论的最优控制问题,当轨线两端均受限时,也可象此处对快速系统那样进行处理,并得到相应的结果.同时,关于贯截条件及乘子的讨论,也仍然有效. 文中附有二个算例.

OPTIMAL CONTROL PROBLEMS WITH CONSTRAINTED CONDITIONS AT BOTH ENDS OF THE TRAJECTORY

In this paper the problems of minimal time control are studied by using the method in 4] for the case when both ends of the trajectory are constrained by some giving manifolds. The necessary and sufficient conditions for optimality are obtained. The boundary conditions of the related systems of differential equations are determined and their geometrical senses, i.e. the transversality conditions, are explained. In addition, the characteristics of the Lagrange multipliers used in this paper are discussed.The method may also be applied to the optimal control problems with constrained conditions at both ends in general sense.