Innovative observer design for nonlinear systems using Caputo fractional derivative with respect to another function
This work introduces a novel control framework using the Caputo fractional derivative (CFD) with respect to another function—a derivative that has not been thoroughly treated in control theory. By extending the widely recognized Caputo-Hadamard (CH) fractional-order derivative, we address its utilit...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241686 |
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| author | Kareem Alanazi Omar Naifar Raouf Fakhfakh Abdellatif Ben Makhlouf |
| author_facet | Kareem Alanazi Omar Naifar Raouf Fakhfakh Abdellatif Ben Makhlouf |
| author_sort | Kareem Alanazi |
| collection | DOAJ |
| description | This work introduces a novel control framework using the Caputo fractional derivative (CFD) with respect to another function—a derivative that has not been thoroughly treated in control theory. By extending the widely recognized Caputo-Hadamard (CH) fractional-order derivative, we address its utility in nonlinear systems. The core of our contribution is the practical stability for systems governed by this derivative, which ensures convergence toward a bounded region around the origin. Additionally, we extend the Lipschitz condition (LC) to the one-sided Lipschitz (OSL) condition for observer design and observer based-control design in fractional-order systems, ensuring its practical stability. Finally, three numerical examples validate the effectiveness of our proposed framework, providing practical insights for control theory advancements. |
| format | Article |
| id | doaj-art-64493973994c47968f59d220522621e7 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-64493973994c47968f59d220522621e72025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912355333555010.3934/math.20241686Innovative observer design for nonlinear systems using Caputo fractional derivative with respect to another functionKareem Alanazi0Omar Naifar1Raouf Fakhfakh2Abdellatif Ben Makhlouf3Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia; Email: k.alanazi@ju.edu.sa, rfakhfakh@ju.edu.saSfax University, Faculty of Sciences of Sfax, Department of Mathematics, BP 1171, Sfax 3000, Tunisia; Email: abdellatif.benmakhlouf@fss.usf.tnDepartment of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia; Email: k.alanazi@ju.edu.sa, rfakhfakh@ju.edu.saSfax University, Faculty of Sciences of Sfax, Department of Mathematics, BP 1171, Sfax 3000, Tunisia; Email: abdellatif.benmakhlouf@fss.usf.tnThis work introduces a novel control framework using the Caputo fractional derivative (CFD) with respect to another function—a derivative that has not been thoroughly treated in control theory. By extending the widely recognized Caputo-Hadamard (CH) fractional-order derivative, we address its utility in nonlinear systems. The core of our contribution is the practical stability for systems governed by this derivative, which ensures convergence toward a bounded region around the origin. Additionally, we extend the Lipschitz condition (LC) to the one-sided Lipschitz (OSL) condition for observer design and observer based-control design in fractional-order systems, ensuring its practical stability. Finally, three numerical examples validate the effectiveness of our proposed framework, providing practical insights for control theory advancements.https://www.aimspress.com/article/doi/10.3934/math.20241686observer-based controlpractical stabilitycfd with respect to another functioncontrolobserver |
| spellingShingle | Kareem Alanazi Omar Naifar Raouf Fakhfakh Abdellatif Ben Makhlouf Innovative observer design for nonlinear systems using Caputo fractional derivative with respect to another function AIMS Mathematics observer-based control practical stability cfd with respect to another function control observer |
| title | Innovative observer design for nonlinear systems using Caputo fractional derivative with respect to another function |
| title_full | Innovative observer design for nonlinear systems using Caputo fractional derivative with respect to another function |
| title_fullStr | Innovative observer design for nonlinear systems using Caputo fractional derivative with respect to another function |
| title_full_unstemmed | Innovative observer design for nonlinear systems using Caputo fractional derivative with respect to another function |
| title_short | Innovative observer design for nonlinear systems using Caputo fractional derivative with respect to another function |
| title_sort | innovative observer design for nonlinear systems using caputo fractional derivative with respect to another function |
| topic | observer-based control practical stability cfd with respect to another function control observer |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241686 |
| work_keys_str_mv | AT kareemalanazi innovativeobserverdesignfornonlinearsystemsusingcaputofractionalderivativewithrespecttoanotherfunction AT omarnaifar innovativeobserverdesignfornonlinearsystemsusingcaputofractionalderivativewithrespecttoanotherfunction AT raouffakhfakh innovativeobserverdesignfornonlinearsystemsusingcaputofractionalderivativewithrespecttoanotherfunction AT abdellatifbenmakhlouf innovativeobserverdesignfornonlinearsystemsusingcaputofractionalderivativewithrespecttoanotherfunction |