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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(ū,(?))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(ū,(?))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.
In this paper, the methods in [2, 3, 4, 5 and 7] are developed to solve a class of quantitative and qualitative differential game problems. For quantitative measures, we propose the optimal strategy The necessary condition of satisfaction is “the extremum principle of both sides.” For the qualitative strategy, the necessary condition of the optimal strategy (ū, (?)) Is also obtained and need not be limited to “small range” as in [1] The equations governing the trajectories that make up the barrier of the barrier are also discussed, as well as some other problems, such as sufficient conditions, the more general form of the target set, the relationship between qualitative measures and controllability problems, etc. It can be seen that this approach is A powerful tool that can be used to solve many types of optimal control and differential game problems. Two examples are attached.