Approximate controllability of network systems

Yassine El Gantouh; Said Hadd; Abdelaziz Rhandi

doi:10.3934/eect.2020091

Article Contents

2021, Volume 10, Issue 4: 749-766. Doi: 10.3934/eect.2020091

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Approximate controllability of network systems

1.
Faculty of Sciences, Department of Mathematics, Ibn Zohr University, Hay Dakhla, BP8106, 80000–Agadir, Morocco
2.
Dipartimento di Ingegneria dell'Informazione, Ingegneria Elettrica e Matematica Applicata, Università degli Studi di Salerno, Via Giovanni Paolo Ⅱ, 132, 84084 Fisciano (Sa), Italy

^* Corresponding author: Abdelaziz Rhandi
^* Corresponding author: Abdelaziz Rhandi

Dedicated to Rainer Nagel on the occasion of his 80th-Birthday

Received: October 2019

Revised: July 2020

Early access: September 2020

Published: December 2021

This work has been supported by the COST Action CA18232. The third author is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Abstract

In this paper, the rich feedback theory of regular linear systems in the Salamon-Weiss sense as well as some advanced tools in semigroup theory are used to formulate and solve control problems for network systems. In fact, we derive necessary and sufficient conditions for approximate controllability of such systems. These criteria, in some particular cases, are given by the well-known Kalman's controllability rank condition.

Keywords:

Boundary systems,
boundary perturbations,
controllability,
network systems,
Kalman's controllability rank condition.

Mathematics Subject Classification: Primary:93B05, 93B70;Secondary:93C73, 93C05, 93B28.

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