Controlabilidad aproximada de sistemas de control semilineales no autónomos con impulsos no instantáneos, retardo no acotado y condiciones no locales
DOI:
https://doi.org/10.37135/ns.01.09.01Palabras clave:
Condiciones no locales , controlabilidad aproximada, ecuaciones semilineales retardadas con retardo infinito, impulsos no instantáneos, técnica de Bashirov et. at, teoría axiomática de Hale-KatoResumen
En este trabajo estudiamos la controlabilidad aproximada de un sistema de control con retardo no acotado, impulso no instantáneo y condiciones no locales. Estos resultados prueban una vez más que la controlabilidad de un sistema lineal se preserva si consideramos los impulsos, las condiciones no locales y los retardos como perturbaciones del mismo, lo cual es muy natural en los problemas de la vida real, nunca los puntos críticos de una ecuación diferencial corresponden exactamente el punto crítico del modelo que representa, lo mismo ocurre con los impulsos, el retardo y las condiciones no locales; son fenómenos intrínsecos al problema real, que muchas veces no son tomados en cuenta al momento de realizar la modelación matemática. Para lograr nuestro resultado, utilizaremos una técnica desarrollada por A. Bashirov et al., que no utiliza teoremas de punto fijo. Por otro lado, como el retardo es infinito, consideramos un espacio de fase que satisface la teoría axiomática propuesta por Hale-Kato para estudiar ecuaciones diferenciales retardadas con retardo no acotado.
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