ON THE OPTIMAL CONTROL OF A PROBLEM OF ENVIRONMENTAL POLLUTION
DOI:
https://doi.org/10.17268/sel.mat.2016.01.03Keywords:
Environmental pollution, Lagrange multiplier, optimality conditionsAbstract
This article is studied the optimal control of distributed parameter systems applied to an environmental pollution problem. The model consists of a differential equation partial parabolic modeling of a pollutant transport in a fluid. The model is considered the speed with which the pollutant spreads in the environment and degradation that suffers the contaminant by the presence of a factor biological inhibitor, which breaks the contaminant at a rate that is not dependent on space and time.
Using the method of Lagrange multipliers is possible to prove the existence solving the problem of control and obtaining optimality conditions for optimal control.
References
S. de F. Arantes; J. Muñoz Rivera, Optimal control theory for ambient pollution, International Journal of Control, volume 83, Issue 11, 2010.
H. T. Banks, Control and Estimation in Distributed Parameter Systems, Siam, Philadelphia, 1992.
V. Barbu, Necessary Conditions for Distributed Control Problems Governed by Parabolic Variational Inequalites. SIAM J. Control and Optimization, Vol. 19, 1981, pp.64-86.
J. A. Chuquipoma, C. A. Raposo, W. D. Bastos, Optimal control problem for deflection plate with crack. Journal of Dynamical and Control Systems, 18, 397-417, 2012.
I. Ekeland, R. Teman, Analyse Convexe et Probl A¨mes Variationelles. Paris, Dunod - Gauthier Villars, 1973.
A. V. Fursikov, Optimal Control of Distributed Systems: Theory and Applications Translations of Mathematical Monographs, volume 187, American Mathematical Society, Moscow, 1999.
H. R, Joshi, Control of the Convective Velocity Coefficient in a Parabolic Problem. Proceeding of World Congress on Nonlinear Analysis, 2005.
J. L. Lions. Controle Optimal des Systemes Gouvern As par des ´ Equations aux Derive A c s Partielles,Dunod - Gauthiers - Villars, Paris 1968.
J. L. Lions. Quelques MA c thodes de Resolution des Problemes aux Limites non Lineaires, Dunod - Gauthiers -Villars, Paris, 1969.
J. L. Lions. Function Spaces and Optimal Control of Distributed Systems, IM-UFRJ, Rio de Janeiro, Brasil, 1980.
J. L. Lions. Some aspects of the Optimal Control of Distributed Parameter Systems, SIAM, Philadelphia, Pennsylvania,1980.
S. Salsa, Partial Differential Equations in Action From Modelling to theory. Springer - Verlag Italia, Milano 2008.
P. Neittaanmaki; D. Tiba, Optimal Control of Nonlinear Parabolic Systems. Theory, Algorithms and Applications,1994.
F. Troltzsch, Optimal Control of Partial Differential Equations Theory, Methods and Applications., Graduate Studies in Mathematics, vol 112, American Mathematical Society, Berlin 2005.
Published
How to Cite
Issue
Section
License
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
