Regional boundary observability for Riemann–Liouville linear fractional evolution systems

Zguaid, Khalid; Alaoui, Fatima-Zahrae El

doi:10.1016/j.matcom.2022.03.023

Cited by 9 publications

(8 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…But first, we give the following result which will be used later. Using ( 8), ( 17), (22), and (24), we can see that ∃R > 0 such that…”

Section: Now Let Us Show the Relative Compactness Ofmentioning

confidence: 99%

“…Finally, the authors gave some numerical simulations to show the efficiency of their methods. As for fractional systems, in previous research [7,[20][21][22][23], authors have investigated the regional observability of linear time-fractional systems with both Riemann-Liouville and Caputo derivatives. They showed that the initial state was successfully recovered in the desired subregion with the help of the HUM approach for fractional systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Regional observability of Caputo semilinear fractional systems

Khalid,

Fatima Zahrae,

Ali

2023

Asian Journal of Control

View full text Add to dashboard Cite

This article studies the problem of regional observability of an important class of time‐fractional evolution systems involving the Caputo time‐fractional derivative. The main goal here is to check the regional observability of the considered system in the desired subregion, , of the evolution domain, . We assume that the linear part of the studied system is approximately regionally observable in the desired subregion , and we add some reasonable hypotheses on the system's dynamic, , as well as on the nonlinear operator . Then, with the help of all these assumptions, we attempt to reconstruct the initial state of our system in the desired subregion . To do that, we propose an extension of the Hilbert uniqueness method (HUM) to semilinear fractional systems. The main advantage of the HUM approach is that it transforms the reconstruction problem into a solvability one, which is more practical. We also present an algorithm for reconstructing the initial state in , which leads to some successful numerical simulations.

show abstract

“…But first, we give the following result which will be used later. Using ( 8), ( 17), (22), and (24), we can see that ∃R > 0 such that…”

Section: Now Let Us Show the Relative Compactness Ofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Regional observability of Caputo semilinear fractional systems

Khalid,

Fatima Zahrae,

Ali

2023

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…In the subject of regional observability, we can already find several works dealing with fractional systems [9,13,[43][44][45][46][47]. However, investigations of regional gradient observability for time-fractional diffusion processes are scarce.…”

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

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.

show abstract

“…In the subject of regional observability, we can already find several works dealing with fractional systems [35][36][37][38][39][40][41]. However, investigations of regional gradient observability for time-fractional diffusion processes are scarce.…”

Section: Introductionmentioning

confidence: 99%

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

Zguaid

Alaoui

Torres

2023

Int. J. Dynam. Control

Self Cite

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 observability for Riemann–Liouville linear fractional evolution systems

Cited by 9 publications

References 9 publications

Regional observability of Caputo semilinear fractional systems

Regional observability of Caputo semilinear fractional systems

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

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

Contact Info

Product

Resources

About