| 基于等级结构的竞争种群系统的最优控制问题 |
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| 引用本文： | 徐阳,赵春. 基于等级结构的竞争种群系统的最优控制问题[J]. 山东大学学报(理学版), 2021, 56(11): 61-70. DOI: 10.6040/j.issn.1671-9352.0.2021.063 |
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| 作者姓名： | 徐阳 赵春 |
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| 作者单位： | 天津师范大学数学科学学院,天津300387 |
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| 基金项目： | 天津市高等学校创新团队培养计划资助项目(TD13-5078) |
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| 摘 要： | 研究了一类基于个体等级结构差异的竞争种群系统最优控制问题。首先利用不动点定理证明了系统解的存在惟一性,其次证明了解对控制变量的连续依赖性,最后通过共轭系统及切锥-法锥的相关理论得出了最优控制的必要性条件。
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| 关 键 词： | 个体等级 种群系统 最优控制 法锥 |
Optimal control of competitive population system with hierarchical structure |
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| XU Yang,ZHAO Chun. Optimal control of competitive population system with hierarchical structure[J]. Journal of Shandong University, 2021, 56(11): 61-70. DOI: 10.6040/j.issn.1671-9352.0.2021.063 |
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| Authors: | XU Yang ZHAO Chun |
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| Affiliation: | College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China |
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| Abstract: | The optimal control problem of a class of competitive population system based on individual level difference is studied. Firstly, the existence and uniqueness of the solution of this system are obtained by the fixed point theorem, then the continuous dependence of the solution on the control variable is proved and the necessary conditions of optimal control can be get by using the concepts of conjugate system and the tangent normal cone theory. |
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| Keywords: | individual level predator-prey system optimal control normal cone |
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