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Regional Enlarged Controllability of Semilinear Systems with Constraints on the Gradient: Approaches and Simulations

  • T. KariteEmail author
  • A. Boutoulout
  • F. Z. El Alaoui
Article
  • 8 Downloads

Abstract

The aim of this paper is to study the constrained gradient controllability problem governed by parabolic evolution equations. The purpose is to find and compute the control u that steers the gradient state from an initial gradient one \(\nabla y_{_{0}}\) to a gradient vector supposed to be unknown between two defined levels \(\alpha (\cdot )\) and \(\beta (\cdot )\), only on a subregion \(\omega \) of the system evolution domain \(\varOmega \). The obtained results have been proved via two approaches: The first one is based on sub-differential techniques, while the second one is based on Lagrangian multipliers. An algorithm is given on the basis of Uzawa algorithm, and numerical results are established.

Keywords

Distributed systems Parabolic systems Regional controllability Gradient Sub-differential Lagrangian multiplier Semilinear systems Minimum energy Uzawa algorithm 

Mathematics Subject Classification

35K58 93B05 93C20 

Notes

Acknowledgements

The present work was supported by Hassan II Academy of Sciences and Technology in Morocco.

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Copyright information

© Brazilian Society for Automatics--SBA 2019

Authors and Affiliations

  1. 1.TSI Team, MACS Laboratory, Department of Mathematics and Computer Science, Institute of SciencesMoulay Ismail UniversityMeknesMorocco

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