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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 304, Pages 298–308
DOI: https://doi.org/10.4213/tm3973
(Mi tm3973)
 

This article is cited in 2 scientific papers (total in 2 papers)

On a Third-Order Singular Arc of Optimal Control in a Minimization Problem for a Mathematical Model of Psoriasis Treatment

E. N. Khailova, E. V. Grigorievab

a Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991 Russia
b Texas Woman's University, 304 Administration Dr., Denton, TX 76204, USA
Full-text PDF (202 kB) Citations (2)
References:
Abstract: A mathematical model of psoriasis treatment is considered on a given time interval. The model consists of three nonlinear differential equations that describe the relationship between the concentrations of T-lymphocytes, keratinocytes, and dendritic cells. The model also includes a bounded control defining the drug dose to suppress the interaction between T-lymphocytes and keratinocytes. For this model, a problem of minimizing the concentration of keratinocytes at the end point of a given time interval is stated. The Pontryagin maximum principle is applied to the analysis of this optimal control problem. For certain relations between the parameters of the model, this principle is used for studying a possible existence of a third-order singular arc of optimal control. Namely, the corresponding necessary optimality condition is verified, and formulas for the optimal solutions of differential equations on this arc are obtained. Finally, a connection of a control on such an arc with nonsingular bang-bang arcs of optimal control is investigated.
Funding agency Grant number
Russian Foundation for Basic Research 18-51-45003 ИНД_a
The work of the first author was supported by the Russian Foundation for Basic Research and by the Department of Science and Technology of the Government of India, project no. 18-51-45003 IND_a.
Received: June 4, 2018
Revised: June 4, 2018
Accepted: January 10, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 304, Pages 281–291
DOI: https://doi.org/10.1134/S0081543819010218
Bibliographic databases:
Document Type: Article
UDC: 517.977.5
Language: Russian
Citation: E. N. Khailov, E. V. Grigorieva, “On a Third-Order Singular Arc of Optimal Control in a Minimization Problem for a Mathematical Model of Psoriasis Treatment”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 298–308; Proc. Steklov Inst. Math., 304 (2019), 281–291
Citation in format AMSBIB
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\paper On a Third-Order Singular Arc of Optimal Control in a Minimization Problem for a Mathematical Model of Psoriasis Treatment
\inbook Optimal control and differential equations
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2019
\vol 304
\pages 298--308
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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