Averaged null controllability for some hyperbolic equations depending on a parameter

Abdelli, Mouna; Hafdallah, Abdelhak

doi:10.1016/j.jmaa.2020.124697

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2023

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“…Te average controllability introduced by Zuazua [7], purpose is to check the averaged state of a parameterized system instead of the state against the unknown parameter. Moreover, the problem of average controllability has recently been introduced in some papers [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Averaged Control Problems Governed by a Semilinear Distributed Systems

Zine

Sidi

Louartassi

et al. 2023

Journal of Mathematics

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In this work, we consider the regional averaged controllability (RAC) problem governed by a class of semilinear hyperbolic systems. We start by giving the definitions of the exact and approximate RAC systems. After that, we state the problem of RAC for semilinear systems. We propose two methods of solution: using a condition of the analytical operator to the nonlinear part of the system to characterize the optimal control via the fixed point theorem and the Hilbert Uniqueness Method (HUM) with an asymptotic condition on the nonlinear part to find the optimal control of the considered problem. Finally, we present a numerical example to show the effectiveness of the main results.

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