Mathematical and Computational Applications | |
Optimal Strategies for Psoriasis Treatment | |
Evgenii Khailov1  Ellina Grigorieva2  | |
[1] MSU Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119992, Russia;TWU Department of Mathematics and Computer Science, Texas Woman’s University, Denton, TX 76204, USA; | |
关键词: psoriasis; nonlinear control system; optimal control; Pontryagin maximum principle; switching function; Lie brackets; singular arc; chattering control; | |
DOI : 10.3390/mca23030045 | |
来源: DOAJ |
【 摘 要 】
Within a given time interval we consider a nonlinear system of differential equations describing psoriasis treatment. Its phase variables define the concentrations of T-lymphocytes, keratinocytes and dendritic cells. Two scalar bounded controls are introduced into this system to reflect medication dosages aimed at suppressing interactions between T-lymphocytes and keratinocytes, and between T-lymphocytes and dendritic cells. For such a controlled system, a minimization problem of the concentration of keratinocytes at the terminal time is considered. For its analysis, the Pontryagin maximum principle is applied. As a result of this analysis, the properties of the optimal controls and their possible types are established. It is shown that each of these controls is either a bang-bang type on the entire time interval or (in addition to bang-bang type) contains a singular arc. The obtained analytical results are confirmed by numerical calculations using the software “BOCOP-2.0.5”. Their detailed analysis and the corresponding conclusions are presented.
【 授权许可】
Unknown