Optimal control of pollution stock

Pages: 578 - 588, Issue Special, September 2011

 Abstract        Full Text (390.7K)              

Ellina Grigorieva - Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204, United States (email)
Evgenii Khailov - Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russian Federation (email)

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. 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
Mathematics Subject Classification:  49J15, 49N90, 93C10, 93C95

Received: July 2010;      Revised: June 2011;      Published: October 2011.