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### 基于等级结构两种群系统的最优初始分布控制

1. 杭州电子科技大学运筹与控制研究所,杭州 310018
• 出版日期:2021-08-25 发布日期:2021-11-23

HE Zerong, ZHOU Nan. Optimal Control of Initial Distributions in a Hierarchical Two Age-Structured Population System[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(8): 2063-2076.

### Optimal Control of Initial Distributions in a Hierarchical Two Age-Structured Population System

HE Zerong, ZHOU Nan

1. Insititute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018
• Online:2021-08-25 Published:2021-11-23

This article concerns an optimal control problem of initial distributions for a class of hierarchical two age-structured population model, in which the state system is described by integro-partial differential equations, and the object functional presents the net profits from the exploitation of the final population distributions. With the proper construction of an adjoint system, the optimal controllers are exactly characterized via normal cones, and the optimal initial distributions must be structured by the truncated function of the adjoint vector. Furthermore, the existence and uniqueness of the optimal strategies are established by means of Ekeland variational principle and fixed point approach. In addition to theoretic analysis, some numerical experiments are conducted to examine the effects of the price functions on the optimal benefits.
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