农作物害虫综合优化治理的数学建模与应用

项目名称： 农作物害虫综合优化治理的数学建模与应用

项目编号： No.11471243

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 裴永珍

作者单位： 天津工业大学

项目金额： 70万元

中文摘要： 基于农作物生育阶段和害虫不同龄期的复合动态经济阈值是害虫防治的量化依据.害虫防治是一个连续或脉冲的动态演化过程,目前与之有关的数学模型已有大量成果，但将以上因素结合到农作物-害虫-天敌构成的复杂生态系统中,研究其最优控制仍然是一项有挑战性的工作.本项目以脉冲治理时间、脉冲干扰强度、经济阈值和时滞等因素为优化参数,以维持生态平衡和农药残留达标为约束条件,以收益最高、治理费用最少和农作物在关键生育期的虫口密度最低为目标函数,建立基于不同治理方式的害虫优化控制动力学模型.分析模型最优控制的存在性,研究最优控制的数值解法.结合实际数据,进行参数估计和模型验证,计算最优经济阈值,给出最优控制策略的数值结果,评价不同治理策略的效果,揭示在农作物的生育期内采用优化的复合动态经济阈值的必要性.该成果将为高维非线性混杂脉冲切换动力系统最优控制的数值计算提供新的思路和方法,为农作物害虫的优化管理提供理论依据.

中文关键词： 害虫管理；优化控制；混杂切换；参数估计；经济阈值

英文摘要： Composite and dynamic economic thresholds in different growth periods of crop and in different of insect stages are the quantitative basis of pest control. Pest management is a continuous or pulse dynamic evolution process. At present there are a lot of achievements in related mathematical modeling. But when considering the above factors to the complex ecosystem of crop-pests-natural enemies, it is a challenge in studying the optimal control strategy of pests. In this research, regarding the pulse control time, the strength of the pulse interfere, economic threshold and time-delay factors as control variables, regarding the ecological balance and pesticide residue as constraint, regarding the largest benefit, the lest cost and the lowest pest density in crucial growth period of crop as the optimization goal, we establish dynamic optimal models based on different methods for pest control. First, the existence of optimal controls is analyzed for each model. Then the numerical algorithms for the optimal control are given. Finally, using the actual data, parameters are estimated and model validation is performed. The optimal economic thresholds are computed, and the numerical results of the optimal control strategy are displayed. Furthermore, we evaluated the effect of different governance policies and revealed the necessity of employing optimal dynamic economic threshold and multi-dimensional threshold to control pests in the crop growing period. The results will provide both new ideas and methods for optimal control of numerical calculation of high-dimensional nonlinear hybrid impulsive and switched dynamic system and theoretical basis for the optimal management of crop pest.

英文关键词： Pest management;Optimal control;Hybrid switch;Parameter estimation;Economic threshold