Analyse régionale des systèmes distribués

Jai, A. El

doi:10.1051/cocv:2002054

Cited by 14 publications

(11 citation statements)

References 43 publications

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“…The operator A with the boundary conditions (24) and initial condition (25) generates an exponentially stable semigroup U.t/ [3,36], that is, (9) and (24), the calculus gives…”

Section: Closed-loop Stabilitymentioning

confidence: 99%

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Distributed control of nonlinear diffusion systems by input–output linearization

Maidi

Corriou

2012

Intl J Robust & Nonlinear

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International audienceThis paper addresses the distributed control by input-output linearization of a nonlinear diffusion equation that describes a particular but important class of distributed parameter systems. Both manipulated and controlled variables are assumed to be distributed in space. The control law is designed using the concept of characteristic index from geometric control by using directly the PDE model without any approximation or reduction. The main idea consists in the control design in assuming an equivalent linear diffusion equation obtained by use of the Cole-Hopf transformation. This framework helps to demonstrate the closed-loop stability using some concepts from the powerful semigroup theory. The performance of the proposed controller is successfully tested, through simulation, by considering a nonlinear heat conduction problem concerning the control of the temperature of a steel plate modeled by a nonlinear heat equation with Dirichlet boundary conditions

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“…The operator A with the boundary conditions (24) and initial condition (25) generates an exponentially stable semigroup U.t/ [3,36], that is, (9) and (24), the calculus gives…”

Section: Closed-loop Stabilitymentioning

confidence: 99%

“…The operator

scriptA

with the boundary conditions and initial condition generates an exponentially stable semigroup U ( t ) , that is,

MathClass-rel∥ U (t) {MathClass-rel∥}_{L^{2} (0 MathClass-punc, l)} ⩽ M e^{MathClass-bin- ω t}

with stability constants M = 1 and ω = α π 2 > 0.…”

Section: Distributed Feedback Designmentioning

confidence: 99%

Distributed control of nonlinear diffusion systems by input–output linearization

Maidi

Corriou

2012

Intl J Robust & Nonlinear

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“…In this paper, we assume that from some a priori knowledge on the source position, it is possible to record the state u at an upstream observation point a and a downstream observation point b with respect to the source position S that 0 < a < S < b < . Besides, we use the concept of a strategic point introduced by El Jai and Pritchard in [7] and employed by the authors in [5,6]. Here, we recall its definition.…”

Section: Mathematical Modelling and Problem Statementmentioning

confidence: 99%

The recovery of a time-dependent point source in a linear transport equation: application to surface water pollution

Hamdi¹

2009

Inverse Problems

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The aim of this paper is to localize the position of a point source and recover the history of its time-dependent intensity function that is both unknown and constitutes the right-hand side of a 1D linear transport equation. Assuming that the source intensity function vanishes before reaching the final control time, we prove that recording the state with respect to the time at two observation points framing the source region leads to the identification of the source position and the recovery of its intensity function in a unique manner. Note that at least one of the two observation points should be strategic. We establish an identification method that determines quasi-explicitly the source position and transforms the task of recovering its intensity function into solving directly a well-conditioned linear system. Some numerical experiments done on a variant of the water pollution BOD model are presented.

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“…Compared to the lumped parameter systems (LPSs), which are described by ordinary differential equations (ODEs), the analysis of the controllability of DPSs is very delicate since several types of controllability exist and it needs sophisticated mathematical tools from functional analysis and semi‐group theory . In addition, for a DPS, this fundamental control property does not depend only on its dynamics described by the PDEs but also on the type (punctual, distributed, or boundary), the geometry and the location of the actuators …”

Section: Introductionmentioning

confidence: 99%

Controllability of nonlinear diffusion system

Maidi

Corriou

2014

Can J Chem Eng

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International audienceIn this article, the semi-group theory is exploited to study the controllability of a particular but important class of distributed parameter systems with a uniform distributed control variable. This class is described by a partial differential equation that characterizes the nonlinear diffusion phenomenon. The main idea consists of using the Cole-Hopf tangent transformation, under some assumptions, in order to derive an equivalent linear model of the nonlinear diffusion system. Then, the study of the controllability of the linear model, based on the semi-group approach, allows us to conclude about the controllability of the nonlinear diffusion system. The study is illustrated by an application example

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Analyse régionale des systèmes distribués

Cited by 14 publications

References 43 publications

Distributed control of nonlinear diffusion systems by input–output linearization

Distributed control of nonlinear diffusion systems by input–output linearization

The recovery of a time-dependent point source in a linear transport equation: application to surface water pollution

Controllability of nonlinear diffusion system

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