一类抛物型系统的快速最优控制

Time Optimal Control for a Class of Parabolic Type Systems

本文讨论较特殊的一类抛物型系统的快速最优控制的问题.利用特征函数展开与泛函分析的方法,对控制区域、初值函数与终值函数作了某些假设的条件下,得到了最优过渡时间的求法及最优控制的存在性、唯一性与极值性.本文所用的方法与所得到的结果也可推广到一类双曲型系统的快速最优控制问题中去.

In thit paper,a problem of time optimal Control for a class of parabolic type systems is discussed.By using Characteristic Functions Expansion and Functional Analysis methods,and under certain assumptions for Control domain, initial and final value functions, solution of optimal transfer time t is obtained. Also are Obtained existence and uniqueness and extremum property of Optimal control. The method and results of this paper can be extended to the problems for a class of hyperbolic type systems as well.