时滞生物偏微分系统最优控制若干问题研究

结题报告

项目介绍

AI项目解读

基本信息

批准号：
11971185
项目类别：
面上项目
资助金额：
52.0万
负责人：
刘斌
依托单位：
华中科技大学
学科分类：
常微分方程
结题年份：
2023
批准年份：
2019
项目状态：
已结题
起止时间：
2019 至 2023

项目参与者：
刘斌；
关键词：
最优必要条件存在性时滞生物数学

项目摘要

This project is a cross topic of biological systems with time delay, partial differential equations and optimal control. It qualitatively studies optimal control of biological partial differential systems with time delay and related issues. The main contents are: to study the optimal control problem of semi-linear predator-prey systems with time delay, to establish the existence and uniqueness conditions of strong solutions of state systems, to obtain the first-order optimal necessary conditions, and to overcome the difficulties caused by time delay; Considering the optimal control problem of quasilinear competitive ecosystem with time delay, the necessary and sufficient conditions for the existence of a global positive strong solution and the existence of first-order and second-order optimal control are discussed. This paper studies the optimal control problem of quasilinear SIS infection system with time-delay repulsive infection tendency, discusses the well-posedness and gives the optimal necessary conditions. The inverse problem of semi-linear SIS epidemic reaction-diffusion system with time delay is discussed, and the first-order optimal necessary conditions are established to realize the numerical simulation results. This paper studies the optimal control problem of SIR parabolic infectious system with time delay, gives the necessary conditions for the second order optimization, and establishes a discrete iterative convergence scheme for the optimal solution. The realization of the research content of this project will help to understand the influence of time delay on optimal control of biological systems and will enrich the theory of optimal control of partial differential equations and the establishment of some optimal control input schemes for biological systems.

本项目是时滞生物系统、偏微分方程、最优控制的交叉课题，定性研究时滞生物偏微分系统最优控制若干问题。主要是：研究半线性具时滞食饵趋向性捕食系统最优控制问题，建立状态系统强解存在唯一性条件、得到一阶最优必要条件，克服时滞所带来的困难；考虑拟线性具时滞竞争生态系统最优控制问题，讨论全局正强解存在唯一条件、建立最优控制存在一阶、二阶最优必要充分条件；研究拟线性具时滞排斥感染趋向性SIS传染系统最优控制问题，讨论适定性、给出最优必要条件；讨论半线性具时滞SIS流行病反应-扩散系统反问题，建立一阶最优必要条件，实现数值仿真结果；研究具时滞SIR抛物型传染系统最优控制问题，给出二阶最优必要条件、建立最优求解的离散迭代收敛方案。本项目研究内容的实现将有助于了解时滞对生物系统最优控制的影响，必将丰富偏微分方程最优控制理论和一些生物系统最优控制输入方案的建立.