caa a22 4500 606233199 CHVBK 20210128101231.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s10883-014-9214-y doi (NATIONALLICENCE)springer-10.1007/s10883-014-9214-y Time Optimal Control Problem for the Waste Water Biotreatment Model [Elektronische Daten] [E. Grigorieva, N. Bondarenko, E. Khailov] 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. Springer Science+Business Media New York, 2014 Biological waste water treatment nationallicence Nonlinear control system nationallicence Time optimal control problem nationallicence Attainable set nationallicence Grigorieva E. Department of Mathematics and Computer Sciences, Texas Woman's University, 76204, Denton, TX, USA aut Bondarenko N. Department of Computational Mathematics and Cybernetics, Moscow State Lomonosov University, 119992, Moscow, Russia aut Khailov E. Department of Computational Mathematics and Cybernetics, Moscow State Lomonosov University, 119992, Moscow, Russia aut Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/1(2015-01-01), 3-24 1079-2724 21:1<3 2015 21 10883 https://doi.org/10.1007/s10883-014-9214-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10883-014-9214-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grigorieva E. Department of Mathematics and Computer Sciences, Texas Woman's University, 76204, Denton, TX, USA aut NATIONALLICENCE 700 1- Bondarenko N. Department of Computational Mathematics and Cybernetics, Moscow State Lomonosov University, 119992, Moscow, Russia aut NATIONALLICENCE 700 1- Khailov E. Department of Computational Mathematics and Cybernetics, Moscow State Lomonosov University, 119992, Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/1(2015-01-01), 3-24 1079-2724 21:1<3 2015 21 10883