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doi: 10.3934/naco.2020055

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

 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

Received  February 2019 Revised  October 2020 Published  November 2020

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 $\Omega$.

Citation: Touria Karite, Ali Boutoulout. Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach. Numerical Algebra, Control & Optimization, doi: 10.3934/naco.2020055
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##### References:
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