害虫控制管理中的最优脉冲控制问题

发布时间：2018-01-29 05:05

本文关键词： 脉冲害虫控制优化算法梯度时间缩放变换混杂优化问题时滞　出处：《天津工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：害虫控制在农业生产中具有重要作用,而微分方程数学模型在描述害虫种群动力学行为中起到了非常重要的作用,特别是用脉冲微分方程来描述害虫种群动力学模型能够更合理、更精确地反映各种变化规律,因为现实世界中害虫的繁殖和危害、以及人类的控制行为几乎都是阶段性的。最优脉冲控制问题一直是一个热点研究课题,脉冲控制将化学防治和生物防治方法结合到一块实现了合理的综合害虫治理目的。本文对害虫治理中的变量优化和时滞优化问题进行了深入分析和研究。第二章节我们研究了害虫增长模型在终端时刻害虫数量最少的最优脉冲管理问题。在优化过程中,通过时间缩放和时间平移技巧,给出了三种情况下目标函数关于天敌最优释放量和释放时间的梯度:优化确定释放时刻下相同的天敌最优释放量(数量控制);优化天敌的最优释放时间和相等但却不确定的最优释放量(时间控制);优化天敌的最优释放时间和非相等的最优释放量(混合控制)。基于梯度公式和设计算法,我们利用数值模拟找到了天敌的最优释放时间和释放量,通过比较显示混合控制策略效果最好,另外证明了优化管理策略可能增加种群的周期震荡幅度,但最终减少了害虫的数量并降低了成本。而且,我们的最优生物干扰策略优于许多文献中在确定时刻释放确定数量天敌的策略。第三章节考虑到目前尚未把寄生卵的滞后寄生、杀虫剂毒杀作用的滞后效应以及投放天敌的年龄等时滞因素看作控制变量,即状态时滞,结合农作物的生育周期,研究农作物在幼苗期、花蕾期、灌浆期等生育期的多特征时间段上的害虫控制模型的优化问题,我们首先提出了一类具有特征时间的状态时滞和参数控制的混杂优化问题,接着给出了涉及的求解优化算法,最后举出两个害虫治理领域的例子说明优化算法的有效性。
[Abstract]:Pest control plays an important role in agricultural production, and the mathematical model of differential equation plays a very important role in describing the behavior of pest population dynamics. In particular, the use of impulsive differential equations to describe pest population dynamics model can be more reasonable and more accurate to reflect the laws of change, because of the propagation and damage of pests in the real world. The optimal pulse control problem is always a hot research topic. Pulse control combines chemical and biological control methods to achieve a reasonable goal of integrated pest control. In this paper, variable optimization and time-delay optimization in pest management are deeply analyzed and studied. In this paper, we study the optimal impulse management problem of the pest growth model with the least number of pests at the end time. Based on the techniques of time scaling and time translation, the optimal release amount and release time gradient of the objective function are given in three cases: the optimal release amount of the same natural enemy (quantity control) is determined by optimizing the release time; Optimizing the optimal release time of the natural enemy and the equal but uncertain optimal release amount (time control); The optimal release time and non-equal optimal release time of natural enemy are optimized. Based on gradient formula and design algorithm, we find the optimal release time and amount of natural enemy by numerical simulation. The comparison shows that the hybrid control strategy has the best effect. In addition, it is proved that the optimal management strategy may increase the periodic fluctuation of the population, but ultimately reduce the number of pests and reduce the cost. Our optimal biological interference strategy is better than that of releasing a certain number of natural enemies at a given time in many literatures. Chapter 3 takes into account that the lagging parasitic eggs have not yet been parasitized. The lag effect of pesticide poisoning and the time delay factors such as the age when the natural enemy was put into the plant were regarded as the control variables, i.e., the state delay. Combining with the growth period of crops, the crops were studied in the seedling stage and the flowering stage. The optimization problem of pest control model in multiple characteristic periods of grain filling stage is discussed. Firstly, we propose a hybrid optimization problem of state delay and parameter control with characteristic time. Finally, two examples in the field of pest control are given to illustrate the effectiveness of the optimization algorithm.
【学位授予单位】：天津工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175;O232

【参考文献】