具有尺度等级和时滞的种群系统的最优边界控制

摘要/Abstract

摘要：

该文基于个体尺度确定的等级差异并考虑孕育期时滞和幼体投放行为，建立了一类种群系统演化控制模型.针对某种预定的理想种群分布，研究最优投放控制问题：适当选取投放策略，使得经过一段指定时间后，种群实际状态与预定分布的差异及执行成本之和最小化.运用特征线方法确立了模型的适定性，借助Ekeland近似极值原理证明了最优策略的存在唯一性，构造恰当的共轭系统并利用法锥结构精细刻画了最优策略，为实际应用奠定理论基础.

关键词: 尺度等级, 时滞, 最优控制, 法锥, 变分原理

Abstract:

In this article, we formulate a population control model, which is based upon the hierarchical size-structure and the incubation delay. For a given ideal population distribution, we investigate the optimal input problem: How to choose a inflow way such that the sum of the deviation between the terminal state and the given one and the total costs is minimal. The well-posedness is established by the method of characteristics, the existence of unique optimal policy is shown by the Ekeland variational principle, and the optimal policy is exactly described by a normal cone and an adjoint system. These results set a foundational framework for practical applications.

Key words: Hierarchy of body size, Delay, Optimal control, Normal cone, Variational principle

中图分类号:

O211.4

何泽荣,窦艺萌,韩梦杰. 具有尺度等级和时滞的种群系统的最优边界控制[J]. 数学物理学报, 2022, 42(3): 867-880.

Zerong He,Yimeng Dou,Mengjie Han. Optimal Boundary Control for a Hierarchical Size-Structured Population Model with Delay[J]. Acta mathematica scientia,Series A, 2022, 42(3): 867-880.

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