Regional boundary gradient observability of semilinear hyperbolic systems via HUM approach

Khazari, Adil; Boutoulout, Ali; Alaoui, Fatima-Zahrae El

doi:10.1093/imamci/dnw036

Cited by 2 publications

(2 citation statements)

References 10 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

View full text Add to dashboard Cite

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

Regional boundary gradient observability of semilinear hyperbolic systems via HUM approach

Cited by 2 publications

References 10 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

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