Regional gradient observability for semilinear hyperbolic systems: HUM approach

Khazari, Adil; Boutoulout, Ali; Harraki, Imad El

doi:10.1007/s11768-018-6122-9

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…For this reason, in the 21th century the notion of regional gradient observability has been introduced and investigated, with the goal of finding and recover the initial gradient vector in a suitable region [39,40]. We adopt here this notion of gradient observability, which has been subject of a recent increase of interest [19,22,23]. This is due to the fact that the concept of gradient observability finds applications in real-life situations.…”

Section: Introductionmentioning

confidence: 99%

Regional Gradient Observability for Fractional Differential Equations with Caputo Time-Fractional Derivatives

Zguaid¹,

Alaoui²,

Torres³

2023

Preprint

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We investigate the regional gradient observability of fractional sub-diffusion equations involving the Caputo derivative. The problem consists of describing a method to find and recover the initial gradient vector in the desired region, which is contained in the spacial domain. After giving necessary notions and definitions, we prove some useful characterizations for exact and approximate regional gradient observability. An example of a fractional system that is not (globally) gradient observable but it is regionally gradient observable is given, showing the importance of regional analysis. Our characterization of the notion of regional gradient observability is given for two types of strategic sensors. The recovery of the initial gradient is carried out using an expansion of the Hilbert Uniqueness Method.Two illustrative examples are given to show the application of the developed approach. The numerical simulations confirm that the proposed algorithm is effective in terms of the reconstruction error.

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Section: Introductionmentioning

confidence: 99%

Regional Gradient Observability for Fractional Differential Equations with Caputo Time-Fractional Derivatives

Zguaid¹,

Alaoui²,

Torres³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…For this reason, in the twenty-first century the notion of regional gradient observability has been introduced and investigated, with the goal of finding and recover the initial gradient vector in a suitable region [16,17]. We adopt here this notion of gradient observability, which has been subject of a recent increase of interest [18][19][20]. This is due to the fact that the concept of gradient observability finds applications in real-life situations.…”

Section: Introductionmentioning

confidence: 99%

Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives

Zguaid

Alaoui

Torres

2023

Int. J. Dynam. Control

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We investigate the regional gradient observability of fractional sub-diffusion equations involving the Caputo derivative. The problem consists of describing a method to find and recover the initial gradient vector in the desired region, which is contained in the spatial domain. After giving necessary notions and definitions, we prove some useful characterizations for exact and approximate regional gradient observability. An example of a fractional system that is not (globally) gradient observable but it is regionally gradient observable is given, showing the importance of regional analysis. Our characterization of the notion of regional gradient observability is given for two types of strategic sensors. The recovery of the initial gradient is carried out using an expansion of the Hilbert uniqueness method. Two illustrative examples are given to show the application of the developed approach. The numerical simulations confirm that the proposed algorithm is effective in terms of the reconstruction error.

show abstract

On the observability of semilinear parabolic systems with constraints on the gradient via HUM approach

Zouiten

Boutoulout

Alaoui

2021

European Journal of Control

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Regional gradient observability for semilinear hyperbolic systems: HUM approach

Cited by 3 publications

References 12 publications

Regional Gradient Observability for Fractional Differential Equations with Caputo Time-Fractional Derivatives

Regional Gradient Observability for Fractional Differential Equations with Caputo Time-Fractional Derivatives

Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives

On the observability of semilinear parabolic systems with constraints on the gradient via HUM approach

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