带时滞的尺度等级结构种群系统的最优初始控制

数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 1181-1191.

带时滞的尺度等级结构种群系统的最优初始控制

何泽荣(),韩梦杰

^{杭州电子科技大学运筹与控制研究所杭州 310018}

收稿日期:2020-06-08 出版日期:2021-08-26 发布日期:2021-08-09
作者简介:何泽荣, E-mail: zrhe@hdu.edu.cn
基金资助:
国家自然科学基金(11871185);浙江省自然科学基金(LY18A010010)

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

Zerong He(),Mengjie Han

^{Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018}

Received:2020-06-08 Online:2021-08-26 Published:2021-08-09
Supported by:
the NSFC(11871185);the NSF of Zhejiang Province(LY18A010010)

摘要/Abstract

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.

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

Abstract:

This article is concerned with an optimal control problem for a hierarchical size-dependent 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.

Key words: Hierarchy of size, Integro-partial differential equations, Optimal control, Normal cones, Variational principle

中图分类号:

O211.4

何泽荣,韩梦杰. 带时滞的尺度等级结构种群系统的最优初始控制[J]. 数学物理学报, 2021, 41(4): 1181-1191.

Zerong He,Mengjie Han. Optimal Control of Initial Distributions in a Hierarchical Size-Structured Population System with Delay[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1181-1191.

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