This paper is concerned with an optimal control problem,in which the state system is described by a nonlinear second-order partial integro-differential equa-tion,the control function stands for initial population distribution,and the index gives the net benefits from the population resources after an arbitrarily fixed time.Based on some conditions on model parameters,we establish the necessary optimality condi-tions(i.e.,maximum principle),which provide the structure of optimal strategies and are given by a truncating function of the adjoint variable.Furthermore,we show that there is one and only one optimal control policy by the means of Ekeland's variational principle and fixed points reasoning of contraction mappings.Numerical experiments display the applicability of the obtained theoretical results.
关键词
随机游动/等级差异/初始分布/最优控制/法锥/变分原理
Key words
Random walks/hierarchy of ages/initial distributions/optimal controls/normal cones/variational principle
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