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Solution of the Feedback Control Problem in the Mathematical Model of Leukaemia Therapy

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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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Acknowledgements

The first author contributed to this paper while visiting Heriot-Watt University as a Distinguished Visiting Professor of the Royal Academy of Engineers. This support is highly appreciated.

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Authors and Affiliations

  1. Lomonosov State University, Leninskie Gory, Moscow, 119991, Russian Federation

    A. Bratus & I. Yegorov

  2. Mannheim University of Applied Sciences, Paul-Wittsack-Str. 10, 68163, Mannheim, Germany

    Y. Todorov

  3. Heriot-Watt University, Edinburgh, EH14 4AS, UK

    D. Yurchenko

Authors
  1. A. Bratus
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  2. Y. Todorov
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  3. I. Yegorov
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  4. D. Yurchenko
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Correspondence to Y. Todorov.

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Bratus, A., Todorov, Y., Yegorov, I. et al. Solution of the Feedback Control Problem in the Mathematical Model of Leukaemia Therapy. J Optim Theory Appl 159, 590–605 (2013). https://doi.org/10.1007/s10957-013-0324-6

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  • DOI: https://doi.org/10.1007/s10957-013-0324-6

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