Optimal Strategies for Psoriasis Treatment

Mathematical and Computational Applications

Khailov, Evgenii¹  Grigorieva, Ellina² 

[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

学科分类：计算数学

来源: mdpi

【 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】

CC BY