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

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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.

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Acknowledgements

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

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  1. TSI Team, MACS Laboratory, Department of Mathematics and Computer Science, Institute of Sciences, Moulay Ismail University, Meknes, Morocco

    T. Karite, A. Boutoulout & F. Z. El Alaoui

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  1. T. Karite
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  2. A. Boutoulout
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  3. F. Z. El Alaoui
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Correspondence to T. Karite.

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Karite, T., Boutoulout, A. & El Alaoui, F.Z. Regional Enlarged Controllability of Semilinear Systems with Constraints on the Gradient: Approaches and Simulations. J Control Autom Electr Syst 30, 441–452 (2019). https://doi.org/10.1007/s40313-019-00460-3

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