摘要:
本文将文献[2,3,4,5,7]中的方法加以发展,用来解决一类定量和定性微分对策问题.
对于定量对策,我们推出最优策略(u,v)所应满足的必要条件,即"双方极值原理".对于定
性对策,也得到最优策略(u,v)的必要条件、且不必如文献[1]中那样限于"小范围".并确定了
组成界栅(barrier)的轨线的方程.
还讨论了一些其他问题,如充分条件、目标集的更一般的形式、定性对策与能控性问题间
的关系等.
可见,这种方法是一种可用来解决多种类型的最优控制和微分对策问题的有力工具.
文中附有二例.
Abstract:
In this paper, by developing the method in [2, 3, 4, 5, 7], we solve the problems
of quantitative and qualitative differential games. For the former, we derive the necessary
condition for optimal strategy (u,v), i.e., the "minimax principle." For
the latter, we also obtain the necessary condition of the optimality of (u,v), and
thereby determine the differential equations of the "barrier". Here we need not
limit our analysis "in the small" as in [1].
We discuss also other problems, such as sufficient condition, the more general terminal
set, and the relation between qualitative differential games and controllability
problems.
Therefore, the method that we used is a powerful one to solve various problems
of optimal control as well as differential games.
Two examples are given.
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