数学物理学报 ›› 2010, Vol. 30 ›› Issue (2): 477-486.

• 论文 • 上一篇    下一篇

具有年龄结构和约束的群落系统的最优收获

何泽荣   

  1. 杭州电子科技大学运筹与控制研究所, 杭州 310018
  • 收稿日期:2008-09-29 修回日期:2009-08-25 出版日期:2010-04-25 发布日期:2010-04-25
  • 基金资助:

    国家自然科学基金(10771048)和浙江省高校中青年学科带头人计划(人才项目)资助.

On Constrained Harvesting for a General Age-structured Model of Interacting Populations

 HE Ze-Rong   

  1. Institute of Operational Research &|Cybernetics, Hangzhou Dianzi University, Hangzhou 310018
  • Received:2008-09-29 Revised:2009-08-25 Online:2010-04-25 Published:2010-04-25
  • Supported by:

    国家自然科学基金(10771048)和浙江省高校中青年学科带头人计划(人才项目)资助.

摘要:

研究一类有年龄结构和相互作用的两种群构成的群落系统的最优收获问题, 要求控制过程结束时的种群状态充分接近预先指定的年龄分布.证明了最优控制的存在性, 运用Dubov- itskii-Milyutin理论导出了最优性条件.这种处理方法为研究连续年龄分布下种群收获问题提供了统一框架.

关键词: 收获, 相互作用, 状态约束, 年龄结构, 最优控制, Dubovitskii-Milyutin定理

Abstract:

The author studies an optimal harvesting problem for a fairly general system modelling the dynamics of two
interacting species, under the constraint that the terminal state must be near a specified-in-advance distribution. The existence of optimal control is established and the optimality conditions in the form of adjoint system and maximum principle are derived via Dubovitskii-Milyutin theory. The  treatment provides a unified approach for harvesting age-dependent multi-species.

Key words: Harvest, Interaction of species, State constraint, Age structure, Optimal control, Dubovitskii-Milyutins theorem

中图分类号: 

  • 35B10