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Published in: Journal of Dynamical and Control Systems 1/2015

01-01-2015

Time Optimal Control Problem for the Waste Water Biotreatment Model

Authors: E. V. Grigorieva, N. V. Bondarenko, E. N. Khailov

Published in: Journal of Dynamical and Control Systems | Issue 1/2015

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Abstract

This work is devoted to solving the time optimal control problem of a mathematical model describing the process of biological waste water treatment and is given as a three-dimensional nonlinear control system of differential equations. For analysis of this problem, the Pontryagin maximum principle is used and the corresponding two-point boundary value problem is formulated. In order to investigate the uniqueness of a solution to this problem, the properties of the corresponding attainable set and the multivalued mapping associated with it are studied. The basis of analysis of this set is its parametric description by moments of switching of piecewise constant controls. A scheme for the approximate solution of the time optimal control problem for the original system is proposed, and results of numerical calculations are presented.

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Metadata
Title
Time Optimal Control Problem for the Waste Water Biotreatment Model
Authors
E. V. Grigorieva
N. V. Bondarenko
E. N. Khailov
Publication date
01-01-2015
Publisher
Springer US
Published in
Journal of Dynamical and Control Systems / Issue 1/2015
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-014-9214-y

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