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基于等级结构两种群系统的最优初始分布控制

何泽荣,周楠   

  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

何泽荣, 周楠. 基于等级结构两种群系统的最优初始分布控制[J]. 系统科学与数学, 2021, 41(8): 2063-2076.

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
研究一类基于个体年龄等级结构的两种群系统模 型的最优初始分布控制问题, 状态系统由偏微分-积分方程 组描述, 目标泛函表征利用两种群终态分布所获得的净收益. 应用凸分析中的锥理论与共轭系统技巧对最优策略作了精确刻画, 运用~Ekeland~变分原理和不动点方法证明了最优控制策略的存在唯一性. 除了理论分析, 还用数值方法考察价格函数对最优收益的影响.
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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