Email this article Reachable Set of a Control Model for Two-Step Wastewater Biotreatment
- Authors: Khailov E.N.1, Grigorieva E.V.2
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Affiliations:
- Faculty of Computation Mathematics and Cybernetics, Lomonosov Moscow State University
- Department of Mathematics and Computer Sciences, Texas Woman’s University
- Issue: Vol 28, No 4 (2017)
- Pages: 572-605
- Section: Article
- URL: https://journal-vniispk.ru/1046-283X/article/view/247663
- DOI: https://doi.org/10.1007/s10598-017-9382-1
- ID: 247663
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Abstract
We consider a mathematical model describing a two-step process of wastewater biotreatment. This is a four-dimensional nonlinear system of differential equations with a scalar constraint on the control. The Pontryagin maximum principle is applied to investigate the boundary of the reachable set in this system. Among the possible parameter values and initial conditions of the model, we identify those for which piecewise-constant controls corresponding to boundary points of the reachable set have at most one, two, and three switching points.
About the authors
E. N. Khailov
Faculty of Computation Mathematics and Cybernetics, Lomonosov Moscow State University
Email: cmm@cs.msu.ru
Russian Federation, Moscow
E. V. Grigorieva
Department of Mathematics and Computer Sciences, Texas Woman’s University
Email: cmm@cs.msu.ru
United States, Denton, TX, 76204
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