一类具有等级结构的种群系统的最优控制  

Optimal control of a class of population system with hierarchical structure

作　　者：徐阳 赵春[1] XU Yang;ZHAO Chun(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2021年第1期1-6,12,共7页Journal of Tianjin Normal University：Natural Science Edition

基　　金：天津市高等学校创新团队培养计划资助项目(TD13-5078).

摘　　要：研究一类基于个体等级差异的种群系统的最优控制问题.首先,利用不动点定理证明了系统解的存在唯一性;其次,利用特征线法和积分不等式证明了解对控制变量的连续依赖性;最后,通过共轭系统和法锥性质得到了最优控制的必要性条件.The optimal control problem of a class of population system based on individual level difference is studied.Firstly,the existence and uniqueness of solution of the system are obtained by using the fixed point theorem.Then the continuous dependence of the solution on the control variable is proved by means of characteristics and integral estimations.Finally,the necessary conditions of optimal control are obtained by using conjugate system and normal cone.

关 键 词：个体等级 种群系统 最优控制 法锥 

分 类 号：O175[理学—基础数学]