带时滞的尺度等级结构种群系统的最优初始控制

Abstract

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

CLC Number:

O211.4

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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References 22

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

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