具年龄和加权的半线性种群系统的最优边界控制

J4 ›› 2013, Vol. 51 ›› Issue (01): 27-33.

具年龄和加权的半线性种群系统的最优边界控制

付军¹, 朱宏²

1. 吉林师范大学数学学院, 吉林四平 136000； 2. 吉林师范大学计算机学院, 吉林四平 136000

收稿日期:2012-05-25 出版日期:2013-01-26 发布日期:2013-01-31
通讯作者: 付军 E-mail:jlfj8080@126.com

Optimal Boundary Control for a Semilinear AgeDependentPopulation System Based on Weight

FU Jun¹, ZHU Hong^2

1. College of Mathematics, Jilin Normal University, Siping 136000, Jilin Province, China;
2. College of Computer, Jilin Normal University, Siping 136000, Jilin Province, China

Received:2012-05-25 Online:2013-01-26 Published:2013-01-31
Contact: FU Jun E-mail:jlfj8080@126.com

摘要/Abstract

摘要：

讨论一类具年龄和加权的半线性种群系统的最优控制问题. 运用Mazur’s定理证明了最优边界控制的存在性, 利用Gteax微分和Lions的变分不等式理论得到了控制为最优的一阶必要条件, 从而得到了由积分偏微分方程和变分不等式构成的最优性组, 该最优性组能确定最优控制.

关键词: 加权种群系统；最优边界控制；一阶必要条件；最优性组

Abstract:

The authors discussed the optimal boundary control for a semilinear age dependent population system based on weight, proved the existence of optimal boundary control via Mazur’s theorem. We obtained the necessary conditions for an optimal control, using Gteax differentiation and Lions’ theory of variational inequalities; and then obtained the optimality system consisting of integral paritial differential equation and variational inequalities. The optimality system can determine optimal control. These results may serve as theoretical reference for practical researches of the control problem in population systems. Its optimality systems determine the optimal control.

Key words: populationweighted system, optimal boundary control, firstorder necessary condition, optimality system

中图分类号:

O231.4

付军, 朱宏. 具年龄和加权的半线性种群系统的最优边界控制[J]. J4, 2013, 51(01): 27-33.

FU Jun, SHU Hong. Optimal Boundary Control for a Semilinear AgeDependentPopulation System Based on Weight[J]. J4, 2013, 51(01): 27-33.