Regional Boundary Observability with Constraints on the State of Semilinear Parabolic Systems

Zouiten, Hayat; Boutoulout, Ali; Alaoui, Fatima-Zahrae El

doi:10.1007/978-3-030-26149-8_19

Cited by 1 publication

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many approaches have been suggested to reconstruct the initial state of a given system, such as HUM [16,26], Lagrangian multiplier approach [27], and sectorial approach [28]. The main objective of this manuscript is to investigate the regional observability of the considered semilinear fractional system.…”

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

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