Actuators and regional boundary controllability of parabolic systems

Zerrik, El Hassan; Boutoulout, Ali; Jai, A. El

doi:10.1080/002077200291479

Cited by 65 publications

(41 citation statements)

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“…The notion of regional controllability for distributed linear systems was introduced by El Jai et al (1995) and consists in steering such a system to a desired state only in a subregion of the system evolution domain. Important developments and several works concerning linear parabolic systems were published (El Jai et al, 1995;Zerrik et al, 2004;Zerrik et al, 2000). Next, Zerrik and Larhrissi extended these results to linear hyperbolic systems and proposed approaches to the computation of the optimal control which allows us to reach a desired target in such a subregion (Zerrik et al, 2001;Zerrik et al, 2002).…”

Section: Introductionmentioning

confidence: 99%

“…Important developments and several works concerning linear parabolic systems were published (El Jai et al, 1995;Zerrik et al, 2004;Zerrik et al, 2000). Next, Zerrik and Larhrissi extended these results to linear hyperbolic systems and proposed approaches to the computation of the optimal control which allows us to reach a desired target in such a subregion (Zerrik et al, 2001;Zerrik et al, 2002). A natural direction is to extend theses results to semilinear distributed hyperbolic systems which constitute an original framework in regional analysis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Output Controllability Problem for Semilinear Distributed Hyperbolic Systems

Zerrik¹,

Larhrissi²,

Bourray³

2007

International Journal of Applied Mathematics and Computer Science

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The paper aims at extending the notion of regional controllability developed for linear systems to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder's fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Output Controllability Problem for Semilinear Distributed Hyperbolic Systems

Zerrik¹,

Larhrissi²,

Bourray³

2007

International Journal of Applied Mathematics and Computer Science

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“…This concept has been widely developed and interesting results have been obtained, in particular, the possibility to reach a state only on an internal subregion  of (El Jai et al [19]) or on a part of the boundary of (Zerrik et al [20]). The principal reason for introducing this concept is that, first it makes sense for the usual controllability concept closer to real world problem and, second, it can be applied to systems which are not controllable on the whole domain.…”

Section: Introductionmentioning

confidence: 99%

Regional Controllability of Semi-Linear Distributed Parabolic Systems: Theory and Simulation

Kamal¹,

Boutoulout²,

Beinane³

2012

ICA

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The aim of this brief paper is to give several results concerning the regional controllability of distributed systems governed by semi-linear parabolic equations. We concentrate on the determination of a control achieving internal and boundary regional controllability. The approach is based on an extension of the Hilbert Uniqueness Method (HUM) and Schauder's fixed point theorem. We give a numerical example developed in internal and boundary sub region. These numerical illustrations show the efficiency of the approach and lead to conjectures.

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“…The regional case was studied by Zerrik et al (2003) [6]. Pussed by the need to control the flux Zerrik et al(1999) [7] developed the gradient controllability of parabolic systems. Our study will be devoted to the regional gradient controllability of the hyperbolic systems.…”

Section: Introductionmentioning

confidence: 99%

Gradient Controllability for Hyperbolic Systems

Bourray¹,

Boutoulout²,

Harraki³

2014

Inf. Sci. Lett.

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This paper deals with the problem of regional gradient controllability of hyperbolic systems. We show how one can reach a desired state gradient given only on a part of the system evolution domain. Also we explore a numerical approach using Hilbert Uniqueness Method (HUM) that leads to an explicit formula of the optimal control. The obtained results are successfully tested through computer simulations leading to some conjectures.

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Actuators and regional boundary controllability of parabolic systems

Cited by 65 publications

References 0 publications

An Output Controllability Problem for Semilinear Distributed Hyperbolic Systems

An Output Controllability Problem for Semilinear Distributed Hyperbolic Systems

Regional Controllability of Semi-Linear Distributed Parabolic Systems: Theory and Simulation

Gradient Controllability for Hyperbolic Systems

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