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Strong and weak output stabilisation for distributed bilinear systems

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Journal of Control and Decision 2021年第3期8卷 314-321页

作者： Abderrahman Ait Aadi el hassan zerrik MACS Laboratory Department of MathematicsUniversity of Moulay IsmailMeknesMorocco

This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain.We give sufficient conditions for strong and weak output ***,the output stabilisation is d... 详细信息

关键词： Bilinear systems output stabilisation feedback controls decay estimate minimisation problem

On the gradient tracking problem for a bilinear reaction–diffusion equation excited by distributed bounded controls

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Journal of Control and Decision 2023年第3期10卷 365-373页

作者： el hassan zerrik Abderrahman Ait Aadi Mohamed Ouhafsaa MACS Laboratory Faculty of SciencesMoulay Ismail UniversityMeknesMorocco Department of Sciences Ecole Normale SupérieureMoulay Ismail UniversityMeknesMorocco

This paper addresses a gradient tracking problem of a bilinear reaction–diffusion equation evolvingin a spatial domainΩ ⊂ Rn, n ≤ 3. Such an equation is excited with distributed and boundedcontrols. The problem is formulated by the minimisation of a functional constituted of the deviationbetween the desired gradient and the current one all over a time interval and the energyterm. Then we prove the existence of an optimal control that we characterise by an optimalitysystem. Moreover, we discuss two sets of particular controls: the set of time dependent controlsand the space dependent ones. A computational approach and illustrative simulations are alsogiven.

关键词： Infinite dimensional systems bilinear systems reaction–diffusion equation controllability optimal control

An Output Stabilization Problem of Distributed Linear Systems Approaches and Simulations

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Intelligent Control and Automation 2012年第2期3卷 159-167页

作者： el hassan zerrik Yassine Benslimane Department of Mathematics and Computer Science Faculty of ScienceUniversity of Moulay IsmailMeknesMorocco

The goal of this paper is to study an output stabilization problem: the gradient stabilization for linear distributed systems. Firstly, we give definitions and properties of the gradient stability. Then we characterize controls which stabilize the gradient of the state. We also give the stabilizing control which minimizes a performance given cost. The obtained results are illustrated by simulations in the case of one-dimensional distributed systems.

关键词： Distributed System Gradient Stability Gradient Stabilization Stabilizing Control

Sensors and Regional Gradient Observability of Hyperbolic Systems

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Intelligent Control and Automation 2012年第1期3卷 78-89页

作者： Samir Benhadid Soraya Rekkab el hassane zerrik MACS Team Department of Mathematics Faculty of Sciences University Moulay Ismail Meknes Morocco Mathematics Department Faculty of Exact Sciences University Mentouri Constantine Algeria

This paper presents a method to deal with an extension of regional gradient observability developed for parabolic system [1,2] to hyperbolic one. This concerns the reconstruction of the state gradient only on a subregion of the system domain. Then necessary conditions for sensors structure are established in order to obtain regional gradient observability. An approach is developed which allows the reconstruction of the system state gradient on a given subregion. The obtained results are illustrated by numerical examples and simulations.

关键词： Distributed Systems Hyperbolic Systems Observability Regional Gradient Observability Sensors Gradient Reconstruction