研究一类具有个体等级差异的种群系统的预设目标调控问题,其中等级由``年长优先原则''所确立, 状态系统为强耦合的非线性偏微分积分方程,性能指标包含终端状态与目标分布的累积均方差和控制总代价.运用切锥法锥理论与共轭系统技巧建立了反馈控制律,借助辅助函数变换证明了最优策略的存在唯一性.

This paper is concerned with an optimal control problem for a hierarchical age-structured population system, in which the rank is determined by elders priority, and the state system is of strongly-coupled nonlinear integro-partial differential equation. The aim is to minimize the sum of the total harvesting costs and deviation between the final state at the end of control and a prescribed population distribution. A feedback (closed-loop) optimal control law is established by means of tangent-normal cones and adjoint system technic, which is convenient for practical applications of the control model. In order to assure that there is one and only one optimal policy, we construct an auxiliary function, which transforms the optimal control problem for the infinite system to a minimizing problem of a function in a real variable. Via the convexity of the admissible control set and the regularities of state and adjoint variables, we obtained the existence of a unique harvesting efforts when the control horizon is short enough.