Diseño de un controlador por realimentación de estados para modelos de dinámica poblacional de plagas ante aplicación periódica de un pesticida

Abstract

Agricultural crops represent a vital part of the global economy and are essential for ensuring food security. Agriculture is responsible for the production of most of the world's food, and it is the largest employer on a global scale, with more than one billion people working in this sector. In Colombia, 15% of the workforce is employed in the agricultural sector, and in 2021 this sector accounted for 15.3% of GDP. However, agricultural crops are constantly under threat from a variety of pests that have a detrimental effect on food production and availability, causing significant economic losses. Aphids, for instance, are a family of pests present in a wide variety of crops, and managing their populations has been a constant challenge for farmers due to their rapid reproductive capacity and adaptability to diverse environments. It is estimated that at least 250 species of aphids are considered pests of economic importance due to their ability to cause significant damage to agricultural crops. Regarding the issue of pest populations, conventional methods such as the application of chemical insecticides are frequently employed. Nevertheless, these methods can be costly and inefficient in the long term due to the development of multiple forms of resistance by pests to these substances. It is imperative for farmers to exercise precision in the application of pesticides, given the potential for pesticide residues to compromise crop quality by altering physicochemical properties, accumulating in soils, and introducing toxicological risks to consumers. In this context, Automatic Control Theory can be applied to formulate pesticide application as an optimization problem, seeking a balance between effective pest suppression and minimal pesticide use. In this thesis, a controller is designed to estimate the periodic use of pesticides in pest population dynamics models based on stability, observability, and controllability analysis, and controller simulation.