Optimal Control of Bistable Traveling Waves: Looking for the Best Spatial Distribution of a Killing Action to Block a Pest Invasion

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-04-22 DOI:10.1137/22m1528410

Luis Almeida, Alexis Léculier, Grégoire Nadin, Yannick Privat

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1291-1315, April 2024.
Abstract. Some pests and vectors of many vector-borne diseases (like mosquitoes for malaria and dengue) are known to invade any homogeneous and favorable territory, following a traveling wave type dynamic. The density of individuals in the field is commonly modeled as the solution of a bistable reaction-diffusion equation on an unbounded domain. In this work, we are interested in finding an optimal strategy to block such a solution by means of a population elimination action in a prescribed subdomain (modeling, for instance, the effect of a mechanical action or an insecticide applied in a certain region to reduce the number of individuals in the population). We propose a complete description of the solutions of this problem, based on the precise analysis of the optimality conditions and on arguments for comparison between the possible strategies.

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双稳态行波的优化控制：寻找阻止害虫入侵的杀戮行动的最佳空间分布

SIAM 控制与优化期刊》第 62 卷第 2 期第 1291-1315 页，2024 年 4 月。摘要众所周知，一些害虫和许多病媒传播疾病的病媒（如疟疾和登革热的蚊子）会按照行波类型的动态入侵任何均质和有利的区域。该领域中的个体密度通常被模拟为无界域上双稳态反应-扩散方程的解。在这项工作中，我们感兴趣的是找到一种最佳策略，通过在规定的子域中采取种群消除行动（例如，模拟在特定区域施加机械行动或杀虫剂以减少种群个体数量的效果）来阻止这种解。我们基于对最优条件的精确分析，以及对各种可能策略进行比较的论证，对这一问题的解决方案提出了完整的描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.