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.
作者
刘荣
何泽荣
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)
出处
《系统科学与数学》
CSCD
北大核心
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。
