离散等级种群系统的能控性与最优控制  

Controllability and optimal control of a discrete hierarchical population system

作　　者：何泽荣[1] 王晶晶 HE Ze-rong;WANG Jing-jing(Institute of Operational Research and Cybernetics,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]杭州电子科技大学运筹与控制研究所,浙江杭州310018

出　　处：《高校应用数学学报（A辑）》2020年第4期431-439,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11871185);浙江省自然科学基金(LY18A010010)。

摘　　要：建立具有离散个体等级差异的种群模型,它是一类高维非线性差分方程组.证明了系统的近似能控性;分析了种群资源的最优收获策略,对几种特殊情形获得了最优策略的具体形式,并用数值方法考察了参数变化对最优策略及最优收益的影响.A discrete hierarchical population model is proposed,which is a nonlinear multidimensional system of difference equations.The system is shown to be approximately controllable,and the optimal harvesting strategies for the population resources are investigated.In some particular situations,the harvest formula are derived.Moreover,the effects of parameters on the optimal policy and optimal benefits are examined.

关 键 词：个体等级 非线性差分系统 能控性 最优收获 Pontryagin原理 

分 类 号：O231.2[理学—运筹学与控制论] O232[理学—数学]