Optimal bounded controls problem for bilinear systems

El Hassan  Zerrik; Nihale El  Boukhari

doi:10.3934/eect.2015.4.221

Article Contents

2015, Volume 4, Issue 2: 221-232. Doi: 10.3934/eect.2015.4.221

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Optimal bounded controls problem for bilinear systems

El Hassan Zerrik^1, and
Nihale El Boukhari^1,

1.
MACS Team, Faculty of Sciences, University Moulay Ismail, Meknes

Received: March 31, 2014

Revised: August 31, 2014

Published: May 2015

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Abstract

The aim of this paper is to study the optimal control problem for finite dimensional bilinear systems with bounded controls. We characterize an optimal control that minimizes a quadratic cost functional using Pontryagin's minimum principle, we derive sufficient conditions of uniqueness from the fixed point theorem, and we develop an algorithm that allows to compute the optimal control and the associated states. Our approach is applied to a cancer treatment by chemotherapy in order to determine the optimal dose of a killing agent.

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Mathematics Subject Classification: Primary: 49K15, 49K30; Secondary: 92C50.

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