论文部分内容阅读
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,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。
Fast optimal control and controllability problems can be studied with different extremum principles, all with accompanying equations. When the target set is the intersection of the origin, the end point or the smooth surface, the boundary conditions of the equation are often not easy to determine, but these places are often the key to solving the above two problems. This paper presents a general method of determining the boundary conditions, and called the “set cover method.” It is the development of the method in [1,2,4]. Identifying the boundary conditions at the above-mentioned special points is useful for both types of problems. For example, it can be used to theoretically explain the “switch” rule, solve the synthesis problem and determine the boundary of the controllable zone. The article gives some examples of applications. This method can also be extended for differential game problem.