Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach

Touria Karite; Ali Boutoulout

doi:10.3934/naco.2020055

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2021, Volume 11, Issue 4: 555-566. Doi: 10.3934/naco.2020055

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Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach

Touria Karite^1, , and
Ali Boutoulout^2,

1.
Department of Electrical engineering & Informatics, National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Route d'Imouzzer, BP 72, Fez, MA
2.
TSI Team, Department of Mathematics, Faculty of Sciences, Moulay Ismail University, BP 11201, Avenue Zitoune, Meknes, MA

^* Corresponding author: Touria Karite
^* Corresponding author: Touria Karite

Received: February 2019

Revised: October 2020

Early access: November 2020

Published: December 2021

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Abstract

The aim of this paper is to study the problem of constrained controllability for distributed parabolic linear system evolving in spatial domain $ \Omega $ using the Reverse Hilbert Uniqueness Method (RHUM approach) introduced by Lions in 1988. It consists in finding the control $ u $ that steers the system from an initial state $ y_{_{0}} $ to a state between two prescribed functions. We give some definitions and properties concerning this concept and then we resolve the problem that relays on computing a control with minimum cost in the case of $ \omega = \Omega $ and in the regional case where $ \omega $ is a part of $ \Omega $.

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Mathematics Subject Classification: Primary: 93B05; 93C05; 93C20; Secondary: 34H05; 49J20.

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