On the regional boundary observability of semilinear time-fractional systems with Caputo derivative

This paper considers the regional boundary observability problem for semilinear time-fractional systems. The main objective is to reconstruct the initial state on a subregion of the boundary of the evolution domain of the considered fractional system using the output equation. We proceed by providin...

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Published in:An international journal of optimization and control 2023-01, Vol.13 (2), p.161-170
Main Authors: Zguaid, Khalid, El Alaoui, Fatima Zahrae
Format: Article
Language:English
Subjects:
Caputo Derivative
Control Theory
Evolution
Fixed Point
HUM Approach
Regional Boundary Observability
Semilinear Fractional Systems
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description This paper considers the regional boundary observability problem for semilinear time-fractional systems. The main objective is to reconstruct the initial state on a subregion of the boundary of the evolution domain of the considered fractional system using the output equation. We proceed by providing a link between the regional boundary observability of the considered semilinear system on the desired boundary subregion, and the regional observability of its linear part, in a well chosen subregion of the evolution domain. By adding some assumptions on the nonlinear term appearing in the considered system, we give the main theorem that allows us to reconstruct the initial state in the well-chosen subregion using the Hilbert uniqueness method (HUM). From it, we recover the initial state on the boundary subregion. Finally, we provide a numerical example that backs up the theoretical results presented in this paper with a satisfying reconstruction error.
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subjects Caputo Derivative
Control Theory
Evolution
Fixed Point
HUM Approach
Regional Boundary Observability
Semilinear Fractional Systems
title On the regional boundary observability of semilinear time-fractional systems with Caputo derivative
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