基于尺度结构的竞争种群系统的最优输入率控制  

Optimal control for inputting rate of a size-structure competitive system

作　　者：申柳肖 赵春[1] SHEN Liu-xiao;ZHAO Chun(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,Chin)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《山东大学学报（理学版）》2018年第7期21-29,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11271104);天津市高等学校创新团队培养计划(TD13-5078)

摘　　要：研究了基于个体尺度结构的竞争种群系统最优输入率控制问题。首先借助不动点定理证明了解的存在唯一性,并由特征线法得到解对控制变量的连续依赖性;其次导出共轭系统并应用Ekeland变分原理获得了最优控制的存在唯一性;最后利用切锥-法锥的概念给出了最优控制的必要性条件。Inputting rate control problems of a size-structure competitive system is studied in this paper. First of all,the existence and uniqueness of the solution of the competitive system are proved with the help of the fixed point theorem. Then by using characteristic method,the continuous dependence of solution on control variable is obtained. Secondly,the existence and uniqueness of the optimal control are discussed by Ekeland variational principle. Finally,the necessary conditions of the optimal control are established by the conception of tangent and normal cone.

关 键 词：个体尺度结构 不动点定理 最优输入率 必要性条件 

分 类 号：O232[理学—运筹学与控制论]