Solution of the feedback control problem in the mathematical model of leukaemia therapy

Alexander Bratus; Y. Todorov; I. Yegorov; Daniil Yurchenko

doi:10.1007/s10957-013-0324-6

Solution of the feedback control problem in the mathematical model of leukaemia therapy

Alexander Bratus, Y. Todorov^*, I. Yegorov, Daniil Yurchenko

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

A mathematical model of leukaemia therapy based on the Gompertzian law of cell growth is investigated. The effect of the medicine on the leukaemia and normal cells is described in terms of therapy functions. A feedback control problem with the purpose of minimizing the number of the leukaemia cells while retaining as much as possible the number of normal cells is considered. This problem is reduced to solving the nonlinear Hamilton-Jacobi-Bellman partial differential equation. The feedback control synthesis is obtained by constructing an exact analytical solution to the corresponding Hamilton-Jacobi-Bellman equation.

Original language	English
Pages (from-to)	590-605
Number of pages	16
Journal	Journal of Optimization Theory and Applications
Volume	159
Issue number	3
DOIs	https://doi.org/10.1007/s10957-013-0324-6
Publication status	Published - 1 Dec 2013

Keywords

Feedback control
Optimal control synthesis
Therapy strategy
Acute myeloid leukemia
JACOBI-BELLMAN EQUATION
TUMOR-GROWTH
OPTIMAL STRATEGY
CHEMOTHERAPY
CANCER

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1007/s10957-013-0324-6

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abstract = "A mathematical model of leukaemia therapy based on the Gompertzian law of cell growth is investigated. The effect of the medicine on the leukaemia and normal cells is described in terms of therapy functions. A feedback control problem with the purpose of minimizing the number of the leukaemia cells while retaining as much as possible the number of normal cells is considered. This problem is reduced to solving the nonlinear Hamilton-Jacobi-Bellman partial differential equation. The feedback control synthesis is obtained by constructing an exact analytical solution to the corresponding Hamilton-Jacobi-Bellman equation.",

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T1 - Solution of the feedback control problem in the mathematical model of leukaemia therapy

AU - Bratus, Alexander

AU - Todorov, Y.

AU - Yegorov, I.

AU - Yurchenko, Daniil

PY - 2013/12/1

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N2 - A mathematical model of leukaemia therapy based on the Gompertzian law of cell growth is investigated. The effect of the medicine on the leukaemia and normal cells is described in terms of therapy functions. A feedback control problem with the purpose of minimizing the number of the leukaemia cells while retaining as much as possible the number of normal cells is considered. This problem is reduced to solving the nonlinear Hamilton-Jacobi-Bellman partial differential equation. The feedback control synthesis is obtained by constructing an exact analytical solution to the corresponding Hamilton-Jacobi-Bellman equation.

AB - A mathematical model of leukaemia therapy based on the Gompertzian law of cell growth is investigated. The effect of the medicine on the leukaemia and normal cells is described in terms of therapy functions. A feedback control problem with the purpose of minimizing the number of the leukaemia cells while retaining as much as possible the number of normal cells is considered. This problem is reduced to solving the nonlinear Hamilton-Jacobi-Bellman partial differential equation. The feedback control synthesis is obtained by constructing an exact analytical solution to the corresponding Hamilton-Jacobi-Bellman equation.

KW - Feedback control

KW - Optimal control synthesis

KW - Therapy strategy

KW - Acute myeloid leukemia

KW - JACOBI-BELLMAN EQUATION

KW - TUMOR-GROWTH

KW - OPTIMAL STRATEGY

KW - CHEMOTHERAPY

KW - CANCER

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DO - 10.1007/s10957-013-0324-6

M3 - Article

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VL - 159

SP - 590

EP - 605

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -

Solution of the feedback control problem in the mathematical model of leukaemia therapy

Abstract

Keywords

UN SDGs

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