|
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
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.
Received: June 4, 2018 Revised: June 4, 2018 Accepted: January 10, 2019
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
Linking options:
https://www.mathnet.ru/eng/tm3973https://doi.org/10.4213/tm3973 https://www.mathnet.ru/eng/tm/v304/p298
|
Statistics & downloads: |
Abstract page: | 303 | Full-text PDF : | 40 | References: | 43 | First page: | 12 |
|