| 一类基于时滞和年龄分布的种群控制问题 |
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| 引用本文： | 何泽荣,刘炎.一类基于时滞和年龄分布的种群控制问题[J].系统科学与数学,2010,30(1):053-059. |
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| 作者姓名： | 何泽荣 刘炎 |
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| 作者单位： | 杭州电子科技大学运筹与控制研究所,杭州,310018 |
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| 基金项目： | 国家自然科学基金(10771048)资助课题 |
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| 摘 要： | 研究一类具有离散时滞和年龄结构的生物种群模型的最优收获策略,其状态方程由一阶偏泛函微分方程描述.运用极值化序列方法和Mazur定理证明了最优控制的存在性,借助非线性泛函分析中的切锥-法锥和共轭系统技巧导出了最优性条件.通过对共轭系统的细致分析,确立了最优控制的唯一性,给出了最优解的特征刻画.
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| 关 键 词： | 种群模型 最优收获 时滞 年龄结构 Euler-Lagrange 条件. |
| 收稿时间： | 2008-8-20 |
| 修稿时间： | 2008-12-8 |
ON A CONTROL PROBLEM FOR A CLASS OF POPULATION SYSTEMS WITH TIME DELAY AND AGE DISTRIBUTION |
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| HE Zerong,LIU Yan.ON A CONTROL PROBLEM FOR A CLASS OF POPULATION SYSTEMS WITH TIME DELAY AND AGE DISTRIBUTION[J].Journal of Systems Science and Mathematical Sciences,2010,30(1):053-059. |
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| Authors: | HE Zerong LIU Yan |
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| Institution: | Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018 |
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| Abstract: | An optimal harvesting problem is considered for a class of population models with discrete delay and continuous age distribution, whose state system is described by a partial functional differential equation. The existence of optimal strategy is proved by means of maximizing sequence and Mazur's theorem, and the first-order optimality conditions are derived out via normal cone and adjoint system techniques. Finally by a detailed analysis for the adjoint system, the uniqueness and the characteristic representation of the optimal controller are given. |
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| Keywords: | Population model optimal harvesting delay age structure Euler-Lagrange conditions |
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