具有合理利用率的资产投资系统的最优控制及数值模拟  

Optimal Control and Numerical Simulation of an Asset Investment System with Reasonable Utilization

作　　者：孔凡亮[1] 张隆[1] 陈星[1] 付丽娜[1] 薛婷婷[1] KONG Fan-liang;ZHANG Long;CHEN Xing;FU Li-na;XUE Ting-ting(School of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830023,China)

机构地区：[1]新疆工程学院数理学院,新疆乌鲁木齐830023

出　　处：《数学的实践与认识》2021年第15期41-49,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11661077);新疆维吾尔自治区高校科研计划项目(XJEDU2021Y048);新疆工程学院科研育人项目(2019xgy672112)。

摘　　要：研究了含有资产合理利用率的非线性资产投资系统的最优控制问题,证明了该系统解的存在唯一性,利用Gronwall不等式证明了系统解关于利用率的连续依赖性,运用Mazur原理和L^(2)空间相对紧性得到了最优解的存在性,利用法锥理论得到了最优解存在的必要性,利用向后有限近似差分方程对结论进行了数值模拟.The optimal control problem of nonlinear asset investment system with rational utilization of assets is studied,the existence and uniqueness of the solution are proved,by using the Gronwall inequality we obtain the continuous dependence of the model solution with the utilization,the existence of the optimal solution is obtained by using Mazur principle and relative compactness of L^(2) space,the necessity of optimal solution is obtained by using the theory of normal cone,the backward finite difference equation is used to simulate the conclusion.

关 键 词：最优控制 相对紧性 法锥 差分方程 

分 类 号：F830[经济管理—金融学] O232[理学—运筹学与控制论]