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Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays

1. Silesian University of Technology, Department of Automatic Control, Akademicka 16, 44101 Gliwice, Poland
2. University of Münster, Institute of Computational and Applied Mathematics, Einsteinstr. 62,48149 Münster, Germany
3. Silesian University of Technology, Department of Automatic Control, Akademicka 16, 44101 Gliwice, Poland

We study some control properties of a class of two-compartmental models of response to anticancer treatment which combines anti-angiogenic and cytotoxic drugs and take into account multiple control delays. We formulate sufficient local controllability conditions for semilinear systems resulting from these models. The control delays are related to PK/PD effects and some clinical recommendations, e.g., normalization of the vascular network. The optimized protocols of the combined therapy for the model, considered as solutions to an optimal control problem with delays in control, are found using necessary conditions of optimality and numerical computations. Our numerical approach uses dicretization and nonlinear programming methods as well as the direct optimization of switching times. The structural sensitivity of the considered control properties and optimal solutions is also discussed.

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Keywords Combined cancer therapy; local controllability; optimal control; control delays

Citation: Jerzy Klamka, Helmut Maurer, Andrzej Swierniak. Local controllability and optimal control for\newline a model of combined anticancer therapy with control delays. Mathematical Biosciences and Engineering, 2017, 14(1): 195-216. doi: 10.3934/mbe.2017013

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