Robust feedback design for combined therapy of cancer

Authors

  • Mazen Alamir

    Corresponding author
    1. Control Systems Department of Gipsa Lab, CNRS-University of Grenoble, Saint-Martin d'Hères, France
    • Correspondence to: Mazen Alamir, Control Systems Department of Gipsa Lab, CNRS-University of Grenoble, 11 rue des mathématiques, 38402, Saint-Martin d'Hères France.

      E-mail: mazen.alamir@grenoble-inp.fr

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SUMMARY

In this paper, a mathematical model for the scheduling of angiogenic inhibitors with a killing agent is used to derive a robust state feedback control for the combined therapy of cancer. Robustness is considered against parameter uncertainties through the solution of the associated Hamilton–Jacobi–Isaacs (HJI) partial differential equation. Unlike open-loop optimal control paradigm, solving the HJI equation provides a guaranteed-cost feedback control and a whole visibility of the achievable performance for any possible initial state within the region of interest and for any predefined level of parameter uncertainties. Numerical investigation is proposed using an existing model that has been partially validated using human data. Copyright © 2012 John Wiley & Sons, Ltd.

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