摘要:
快速最优控制及能控性问题均可用不同的极值原理进行研究[1,2,3],均有伴随方程.当目
标集为原点、端点或光滑曲面的交点时,伴随方程的边界条件常不易确定,而这些地方却往往
是求解上述两种问题的关键.本文提出一种确定边界条件的一般方法,并称"集合覆盖法".
它是文[1,2,4]中方法的发展.
确定出上述特殊点处的边界条件,对两种问题都很有用.例如可用来从理论上说明"开
关"规律,解综合问题以及确定能控区边界等.文中给出了一些应用的例子.
这种方法还可扩展用于微分对策问题.
Abstract:
Both the time optimal and controllability problems can be investigated by different
Maximum Principles and both have adjoint equations. When 'the target sets are origin.
terminal point, or the intersection of smooth surfaces, the boundary conditions of the
adjoint equations are not easy to determine. These places are often to be the cruxes for
solving the problems. In this paper, a general method for determining the boundary
conditions is presented. It can be called "The Sets Covering Method" which is the further
development of the method in [1, 2, 4].
The determination of boundary conditions at the above mentioned special points is
very useful for both problems. For instance, it may be used to explain the "switch law"
theoretically, to find the synthesis functions and to determine the boundary of controllable
region, etc.. Several examples are given.
This method can also be extended to solve problems of differential games.
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