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.

scholarly journals Optimal problem of cost function for the linear neutral systems

2001 ◽  
Vol 25 (12) ◽  
pp. 777-785
Author(s):  
Jong Yeoul Park ◽  
Yong Han Kang
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cost Function ◽  
Optimal Condition ◽  
Neutral Type ◽  
Neutral Systems ◽  
Quadratic Cost ◽  
Quadratic Cost Function

We study the optimal control problem of a system governed by linear neutral type in Hilbert spaceX. We investigate optimal condition for quadratic cost function and as applications, we give some examples.

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