Regional optimal control problem with minimum energy for a class of bilinear distributed systems

Zine, Rabie; Sidi, Maawiya Ould

doi:10.1093/imamci/dnx022

Cited by 5 publications

(3 citation statements)

References 13 publications

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“…The paper opens a wide way of research studying other types of semi-linear or nonlinear systems. The proposed method can be generalized to the case of hyperbolic distributed systems, the average controllability of hyperbolic systems can be considered as in [11][12][13].…”

Section: Discussionmentioning

confidence: 99%

Regional averaged control problems with minimum energy constrained by distributed parabolic systems

Sidi¹,

Zine²,

Mohamed³

2021

J. Math. Computer Sci.

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This paper study the regional average controllability problems governed by distributed parabolic systems. We establish the definition and characterization of a system which is regional averaged controllable. The averaged regional control problem with minimum energy is considered and solved using HUM (Hilbert uniqueness method). Thereafter, the case of regional gradient averaged controllability is treated.

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Section: Discussionmentioning

confidence: 99%

Regional averaged control problems with minimum energy constrained by distributed parabolic systems

Sidi¹,

Zine²,

Mohamed³

2021

J. Math. Computer Sci.

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“…Zerrik and Ould Sidi in [12][13][14]) use quadratic control problems to steer the position of infinite-dimensional bilinear systems to the desired state on specific sub-region. Zine and Ould Sidi in [15,16] treated quadratic control problems in the case of hyperbolic bi-linear systems.…”

Section: Introductionmentioning

confidence: 99%

Variational necessary conditions for optimal control problems

Sidi¹

2020

J. Math. Computer Sci.

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“…El Harraki and Boutoulout in [16] studied the controllability of the wave equation with multiplicative controls. Zine and Ould Sidi in [17,18] and Zine in [19] treated the regional optimal control problems governed by bilinear hyperbolic distributed systems.…”

Section: Introductionmentioning

confidence: 99%

Regional gradient optimal control problem governed by a distributed bilinear systems

Sidi¹,

Beinane²

2019

TELKOMNIKA

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This paper gives an extension of previous work on gradient optimal control of distributed parabolic systems to the case of distributed bilinear systems which are a type of nonlinear systems. We introduce the notion of flux optimal control of distributed bilinear systems. The idea is trying to achieve a neighborhood of the gradient state of the considered system by minimizing a nonlinear quadratic cost. Using optimization techniques, a method showing how to reach a desired flux at a final time, only on internal subregion of the system domain will be proposed. The proposed simulation illustrates the theoretical approach by commanding the heat bilinear equation flux to a desired profile.

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Regional optimal control problem with minimum energy for a class of bilinear distributed systems

Cited by 5 publications

References 13 publications

Regional averaged control problems with minimum energy constrained by distributed parabolic systems

Regional averaged control problems with minimum energy constrained by distributed parabolic systems

Variational necessary conditions for optimal control problems

Regional gradient optimal control problem governed by a distributed bilinear systems

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