New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems
In the last few years, a new class of fractional-order (FO) systems, known as Katugampola FO systems, has been introduced. This class is noteworthy to investigate, as it presents a generalization of the well-known Caputo fractional-order systems. In this paper, a novel lemma for the analysis of a fu...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-05-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/11/1814 |
| _version_ | 1827664741623922688 |
|---|---|
| author | Omar Kahouli Assaad Jmal Omar Naifar Abdelhameed M. Nagy Abdellatif Ben Makhlouf |
| author_facet | Omar Kahouli Assaad Jmal Omar Naifar Abdelhameed M. Nagy Abdellatif Ben Makhlouf |
| author_sort | Omar Kahouli |
| collection | DOAJ |
| description | In the last few years, a new class of fractional-order (FO) systems, known as Katugampola FO systems, has been introduced. This class is noteworthy to investigate, as it presents a generalization of the well-known Caputo fractional-order systems. In this paper, a novel lemma for the analysis of a function with a bounded Katugampola fractional integral is presented and proven. The Caputo–Katugampola fractional derivative concept, which involves two parameters 0 < α < 1 and ρ > 0, was used. Then, using the demonstrated barbalat-like lemma, two identification problems, namely, the “Fractional Error Model 1” and the “Fractional Error Model 1 with parameter constraints”, were studied and solved. Numerical simulations were carried out to validate our theoretical results. |
| first_indexed | 2024-03-10T01:06:09Z |
| format | Article |
| id | doaj.art-1b4040dda80e428b9ba73795a427ede5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:06:09Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1b4040dda80e428b9ba73795a427ede52023-11-23T14:24:58ZengMDPI AGMathematics2227-73902022-05-011011181410.3390/math10111814New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification ProblemsOmar Kahouli0Assaad Jmal1Omar Naifar2Abdelhameed M. Nagy3Abdellatif Ben Makhlouf4Department of Electronics Engineering, Community College, University of Ha’il, Ha’il 2440, Saudi ArabiaControl and Energy Management Laboratory, National School of Engineering, Sfax University, BP 1173, Sfax 3038, TunisiaControl and Energy Management Laboratory, National School of Engineering, Sfax University, BP 1173, Sfax 3038, TunisiaDepartment of Mathematics, Faculty of Science, Kuwait University, Safat 13060, KuwaitDepartment of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72311, Saudi ArabiaIn the last few years, a new class of fractional-order (FO) systems, known as Katugampola FO systems, has been introduced. This class is noteworthy to investigate, as it presents a generalization of the well-known Caputo fractional-order systems. In this paper, a novel lemma for the analysis of a function with a bounded Katugampola fractional integral is presented and proven. The Caputo–Katugampola fractional derivative concept, which involves two parameters 0 < α < 1 and ρ > 0, was used. Then, using the demonstrated barbalat-like lemma, two identification problems, namely, the “Fractional Error Model 1” and the “Fractional Error Model 1 with parameter constraints”, were studied and solved. Numerical simulations were carried out to validate our theoretical results.https://www.mdpi.com/2227-7390/10/11/1814fractional-order systemsbounded Katugampola fractional integralCaputo–Katugampola fractional derivativeidentification |
| spellingShingle | Omar Kahouli Assaad Jmal Omar Naifar Abdelhameed M. Nagy Abdellatif Ben Makhlouf New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems Mathematics fractional-order systems bounded Katugampola fractional integral Caputo–Katugampola fractional derivative identification |
| title | New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems |
| title_full | New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems |
| title_fullStr | New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems |
| title_full_unstemmed | New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems |
| title_short | New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems |
| title_sort | new result for the analysis of katugampola fractional order systems application to identification problems |
| topic | fractional-order systems bounded Katugampola fractional integral Caputo–Katugampola fractional derivative identification |
| url | https://www.mdpi.com/2227-7390/10/11/1814 |
| work_keys_str_mv | AT omarkahouli newresultfortheanalysisofkatugampolafractionalordersystemsapplicationtoidentificationproblems AT assaadjmal newresultfortheanalysisofkatugampolafractionalordersystemsapplicationtoidentificationproblems AT omarnaifar newresultfortheanalysisofkatugampolafractionalordersystemsapplicationtoidentificationproblems AT abdelhameedmnagy newresultfortheanalysisofkatugampolafractionalordersystemsapplicationtoidentificationproblems AT abdellatifbenmakhlouf newresultfortheanalysisofkatugampolafractionalordersystemsapplicationtoidentificationproblems |