American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 578-588. doi: 10.3934/proc.2011.2011.578

Optimal control of pollution stock

Ellina Grigorieva 1, and  Evgenii Khailov 2,

1. 

Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204
2. 

Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992

Received  July 2010 Revised  June 2011 Published  October 2011

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. 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: nonlinear model, environmental problem, optimal control.
Mathematics Subject Classification: 49J15, 49N90, 93C10, 93C95.
Citation: Ellina Grigorieva, Evgenii Khailov. Optimal control of pollution stock. Conference Publications, 2011, 2011 (Special) : 578-588. doi: 10.3934/proc.2011.2011.578
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