具有尺度结构的种群混合系统的最优投放控制  

Optimal Throwing Control for a Hybrid Size-Structured Population System

作　　者：刘荣 何泽荣[2] LIU Rong;HE Zerong(School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006;Institute of Operational Research and Cybernetics,Hangzhou Dianzi University,Hangzhou 310018)

机构地区：[1]山西财经大学应用数学学院,太原030006 [2]杭州电子科技大学运筹与控制研究所,杭州310018

出　　处：《系统科学与数学》2023年第8期1969-1981,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12001341,11871185)资助课题。

摘　　要：研究一类具有尺度结构的害鼠种群最优不育控制问题,状态系统模型由一个带全局反馈边界条件的一阶偏微分方程和两个常微分方程组成,控制函数为时变不育剂投放量,性能指标代表害鼠终端规模、环境中不育剂残留量以及控制成本的加权和.首先确立状态系统非负有界解的存在唯一性,并给出状态向量函数关于控制变量的连续依赖性;其次构造共轭系统和关联法锥,导出精确刻画最优策略的Euler-L agrange方程;最后运用Ekeland变分原理和不动点方法证明最优策略的存在唯一性.文章为害鼠不育控制提供一种新的建模方法.This paper is concerned with an optimal contraception control problem for a size-structured vermin population.The state system model consists of a first-order partial differential equation with a global feedback boundary condition and two ordinary differential equations,and the control function is taken to be throwing amount of contraception medicaments.Firstly,the existence of a unique non-negative bounded solution to the state system is established,and the continuous dependence of solutions on the control variable is shown.Then,the Euler-Lagrange equations describing the exact structure of the optimal strategies are derived by constructing a proper adjoint system and relative normal cone.Finally,the existence of a unique optimal policy is proved via Ekeland's variational principle and fixed-point method.This work supplies a novel modelling approach for contraception control of vermin.

关 键 词：尺度结构 混合系统 最优控制 法锥 EKELAND变分原理 

分 类 号：O232[理学—运筹学与控制论]