1409-2433 1409-2433 S1409-24332011000100007 U.S.A Russia 00 06 2011 00 06 2011 18 1 77 109

Optimal control of pollution stock through ecological interaction of the manufacturer and the state

Control óptimo de contaminación almacenada a través de interacción ecológica entre el fabricante y el estado
Ellina V. Grigorieva*
Evgenii N. Khailov†
E.I. Kharitonova‡

*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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Correspondencia a: Ellina V. Grigorieva. Department of Mathematics and Computer Sciences, Texas Woman’s University, Denton, TX 76204, U.S.A. E-Mail: EGrigorieva@mail.twu.edu
Evgenii N. Khailov. Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russia. E-Mail: khailov@cs.msu.su ]]> E.I. Kharitonova. Misma direccin que/same address as E.N. Khailov
Received: 24 Sep 2010; Revised: 19 Nov 2010; Accepted: 26 Nov 2010
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