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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.18 n.1 San José Jun. 2011
Control óptimo de contaminación almacenada a través de interacción ecológica entre el fabricante y el estado
*Department of Mathematics and Computer Sciences, Texas Woman’s University, Denton, TX 76204, U.S.A. E-Mail: EGrigorieva@mail.twu.edu
†Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russia. E-Mail: khailov@cs.msu.su
‡Misma direccin que/same address as E.N. Khailov.
Dirección para correspondencia
Abstract
A model of an interaction between a manufacturer and the state where the manufacturer produces a single product and the state controls the level of pollution is created and investigated. A local economy with a stock pollution problem that must choose between productive and environmental investments (control functions) is considered. The model is described by a nonlinear system of two differential equations with two bounded controls. The best optimal strategy is found analytically with the use of the Pontryagin Maximum Principle and Green’s Theorem.
Keywords: optimal control, nonlinear model, environmental problem.
Resumen
Se ha creado e investigado un modelo de interaccin entre un fabricante y el estado donde el fabricante produce un solo producto y el estado controla el nivel de contaminación. Se considera una economía local con un problema de contaminación almacenada, que debe escoger entre inversiones en producción y medio ambiente (funciones de control). El modelo es descrito por un sistema de dos ecuaciones diferenciales con dos controles acotados. La mejor estrategia de control se encuentra analíticamente usando el Principio del Máximo de Pontryagin y el Teorema de Green.
Palabras clave: control óptimo, modelo no lineal, problema ambiental.
Mathematics Subject Classification: 49J15, 49N90, 93C10, 93C95.
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References
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E.I. Kharitonova. Misma direccin que/same address as E.N. Khailov
Received: 24 Sep 2010; Revised: 19 Nov 2010; Accepted: 26 Nov 2010
