相空间坐标受限时的最优控制问题

对于相空间坐标受限的最优控制问题,P.B.加姆克列利德泽等得到了控制最优性的必要条件(即熟知的极大值原理)和衔接点处的“跳跃条件”.但是文献1]中所用的数学工具不是初等的,推证过程也较繁长,不易为工程技术界所理解.本文在应用文献1]中某些分析的基础上,采用文献2,3]中的方法处理这一问题,作法较为简单,而且除了得到1]中的结论外,还可得到一些新的结果,例如,文中所得到的某些充分条件以及对于线性系统“小范围”最优性的必要充分条件等.

OPTIMAL CONTROL PROBLEM WITH RESTRICTED PHASE COORDINATES

For the problem of optimal control with restricted phase coordinates R. V.Gamkrelidze et al. obtained the necessary condition for optimality and the "jump con-ditions" at the jointed points of optimal trajectory. Since the mathematical tools used in their proof are not elementary, their method is somewhat difficult to understand by engineers.In this paper, based on some analyses in 1], the problem is treated by using the method in 2, 3]. The chief results given in 1] are also obtained rather simply and, in addition, some new results, i.e., some sufficient conditions and the necessary and suffi-cient condition for optimality "in the small" for linear system, are obtained.