Optimization of Combined Leukemia Therapy by Finite-Dimensional Optimal Control Modeling

2017 ◽  
Vol 175 (1) ◽  
pp. 218-235 ◽  
Author(s):  
Svetlana Bunimovich-Mendrazitsky ◽  
Benzion Shklyar
Keyword(s):  
Optimal Control ◽  
Finite Dimensional ◽  
Control Modeling

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 The Natural Gas Cash-Out Problem: A Bilevel Optimal Control Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Vyacheslav V. Kalashnikov ◽  
Francisco Benita ◽  
Patrick Mehlitz
Keyword(s):  
Optimal Control ◽  
Natural Gas ◽  
Mixed Integer ◽  
Integer Programming Problem ◽  
Control Approach ◽  
Finite Dimensional ◽  
Upper Level ◽  
Pure State Constraints ◽  
Mixed Integer Programming Problem ◽  
Theoretical Results

The aim of this paper is threefold: first, it formulates the natural gas cash-out problem as a bilevel optimal control problem (BOCP); second, it provides interesting theoretical results about Pontryagin-type optimality conditions for a general BOCP where the upper level boasts a Mayer-type cost function and pure state constraints, while the lower level is a finite-dimensional mixed-integer programming problem with exactly one binary variable; and third, it applies these theoretical results in order to find possible local minimizers of the natural gas cash-out problem.

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