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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (4): 29-39.doi: 10.6040/j.issn.1671-9352.0.2024.168

• • 上一篇    

具有交叉扩散的植被模型的稀疏最优控制

梁娟1,张晋珠1*,崔亮2   

  1. 1.太原工业学院理学系, 山西 太原 030008;2.山西财经大学资源环境学院, 山西 太原 030006
  • 发布日期:2025-04-08
  • 通讯作者: 张晋珠(1969— ),女,教授,博士,研究方向为动力系统稳定性. E-mail:zhangjinzhu2@yahoo.com.cn
  • 作者简介:梁娟(1987— ),女,副教授,博士,研究方向为生物数学、动力系统稳定性. E-mail:liangjuan76@126.com*通信作者:张晋珠(1969— ),女,教授,博士,研究方向为动力系统稳定性. E-mail:zhangjinzhu2@yahoo.com.cn
  • 基金资助:
    国家自然科学基金资助项目(42075029);山西省基础研究计划项目(202203021212327,202203021211213);太原工业学院引进人才科研资助项目(2024KJ012);第四届太原工业学院学科带头人计划项目

Sparse optimal control of a vegetation model with cross diffusion

LIANG Juan1, ZHANG Jinzhu1*, CUI Liang2   

  1. 1. Department of Science, Taiyuan Institute of Technology, Taiyuan 030008, Shanxi, China;
    2. College of Resources and Environment, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China
  • Published:2025-04-08

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摘要： 建立了一类具有交叉扩散的植被-水反应扩散模型,将人类活动作为控制函数,研究了该植被模型的稀疏最优控制问题,从控制相关的植被斑图形成的角度揭示了如何通过人类活动提高生态系统的稳健性。给出了模型产生图灵斑图的条件,推导了一阶必要最优条件。最后通过数值模拟,从控制效果、 控制误差和控制成本 3 方面验证了该控制方法的合理性以及控制策略的有效性。

关键词: 植被斑图, 荒漠化, 稳健性, 最优控制, 稀疏控制

Abstract: A vegetation-water reaction-diffusion model with cross diffusion is established and human activities are chosen as the control function. The sparse optimal control problem of the model is studied which reveals how to improve the robustness of the ecosystem through human activities from the perspective of controlling the formation of vegetation pattern. Firstly, the conditions for generating Turing pattern are given. Furthermore, the first order necessary optimality condition is derived. Finally, the rationality of the control method and the effectiveness of the control strategy are verified in terms of the control effect, control error and control cost by numerical simulations.

Key words: vegetation pattern, desertification, robustness, optimal control, sparse control

中图分类号: 

  • O175
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