带时滞的尺度等级结构种群系统的最优初始控制  

Optimal Control of Initial Distributions in a Hierarchical Size-Structured Population System with Delay

作　　者：何泽荣[1] 韩梦杰 He Zerong;Han Mengjie(Institute of Operational Research and Cybernetics,Hangzhou Dianzi University,Hangzhou 310018)

机构地区：[1]杭州电子科技大学运筹与控制研究所,杭州310018

出　　处：《数学物理学报（A辑）》2021年第4期1181-1191,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11871185);浙江省自然科学基金(LY18A010010)。

摘　　要：该文以初始分布为控制手段,关注一类具有时滞的尺度等级结构种群系统的最优控制问题,期望控制过程结束时种群分布与目标最接近且成本最低.运用特征线法和先验估计建立了状态关于控制函数的一致连续性,构造法锥和共轭系统导出最小值原理,借助Ekeland变分原理和不动点方法证明了最优解的存在唯一性.这些结果为实际应用奠定了一定的基础.This article is concerned with an optimal control problem for a hierarchical sizedependent population model with delay,the control function is the initial distribution.It is expected that the difference between the terminal state and the given target can be minimized in a least costs.The uniform continuity of states in controls is established by the method of characteristic lines and priori estimates,the minimal principle is derived by the construction of a normal cone and an adjoint system,and the existence of unique optimal strategy is proved by means of the Ekeland variational theorem and fixed-point approach.These results pave the way to applications.

关 键 词：尺度等级 偏泛函微分积分方程 最优控制 法锥 变分原理 

分 类 号：O211.4[理学—概率论与数理统计]