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

Author

Listed:
  • A. Bratus

    (Lomonosov State University)

  • Y. Todorov

    (Mannheim University of Applied Sciences)

  • I. Yegorov

    (Lomonosov State University)

  • D. Yurchenko

    (Heriot-Watt University)

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.

Suggested Citation

  • A. Bratus & Y. Todorov & I. Yegorov & D. Yurchenko, 2013. "Solution of the Feedback Control Problem in the Mathematical Model of Leukaemia Therapy," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 590-605, December.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:3:d:10.1007_s10957-013-0324-6
    DOI: 10.1007/s10957-013-0324-6
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