Optimal Control for Cancer Chemotherapy under Tumor Heterogeneity

2019 ◽  
Author(s):  
Shuo Wang
Keyword(s):  
Optimal Control ◽  
Cancer Chemotherapy ◽  
Tumor Heterogeneity

Constrained bilinear control problem: Application to a cancer chemotherapy model

2017 ◽  
Vol 10 (04) ◽  
pp. 1750054 ◽  
Author(s):  
El Hassan Zerrik ◽  
Nihale El Boukhari
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Cancer Chemotherapy ◽  
Sufficient Conditions ◽  
Treatment Protocol ◽  
Bilinear Model ◽  
Bilinear Control ◽  
Finite Dimensional ◽  
Quadratic Cost ◽  
Admissible Controls

The aim of this paper is to investigate the optimal control problem for finite-dimensional bilinear systems and its application to a chemotherapy model. We characterize an optimal control that minimizes a quadratic cost functional in two cases of constrained admissible controls, then we give sufficient conditions for the uniqueness of such a control, and we derive useful algorithms for the computation of the optimal control. The established results are applied to a cancer chemotherapy bilinear model in order to simulate the optimal treatment protocol using two different approaches: one based on a limited instant toxicity, and the other on a limited cumulative toxicity along the therapy session.

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