具有尺度等级和时滞的种群系统的最优边界控制

Abstract

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

CLC Number:

O211.4

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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References 24

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Optimal Boundary Control for a Hierarchical Size-Structured Population Model with Delay

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