具年龄和加权的半线性种群系统的最优边界控制  

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

作　　者：付军[1] 朱宏[2] 

机构地区：[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

出　　处：《吉林大学学报（理学版）》2013年第1期27-33,共7页Journal of Jilin University:Science Edition

基　　金：吉林省自然科学基金(批准号:201115222);吉林师范大学研究生创新项目(批准号:201114)

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.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 Ggteax 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.

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 

分 类 号：O231.4[理学—运筹学与控制论]