Some results regarding observability and initial state reconstruction for time-fractional systems
The aim of this study is to present the notion of observability for a specific class of linear time-fractional systems of Riemann-Liouville type with a differentiation order between 1 and 2. To accomplish this goal, we first define the concept of observability and its features, then we extend the H...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Balikesir University
2024-03-01
|
| Series: | An International Journal of Optimization and Control: Theories & Applications |
| Subjects: | |
| Online Access: | http://www.ijocta.org/index.php/files/article/view/1468 |
| _version_ | 1797254210278916096 |
|---|---|
| author | Hamza Ben Brahim Fatima-Zahrae El Alaoui Khalid Zguaid |
| author_facet | Hamza Ben Brahim Fatima-Zahrae El Alaoui Khalid Zguaid |
| author_sort | Hamza Ben Brahim |
| collection | DOAJ |
| description |
The aim of this study is to present the notion of observability for a specific class of linear time-fractional systems of Riemann-Liouville type with a differentiation order between 1 and 2. To accomplish this goal, we first define the concept of observability and its features, then we extend the Hilbert Uniqueness Method (HUM) to determine the system's initial state. This method converts the reconstruction problem into a solvability one, leading to an algorithm that calculates the initial state. The effectiveness of the proposed algorithm is demonstrated through numerical simulations, which are presented in the final section.
|
| first_indexed | 2024-04-24T21:46:20Z |
| format | Article |
| id | doaj.art-eb27aed4c7e348f9b0ed33e256212510 |
| institution | Directory Open Access Journal |
| issn | 2146-0957 2146-5703 |
| language | English |
| last_indexed | 2024-04-24T21:46:20Z |
| publishDate | 2024-03-01 |
| publisher | Balikesir University |
| record_format | Article |
| series | An International Journal of Optimization and Control: Theories & Applications |
| spelling | doaj.art-eb27aed4c7e348f9b0ed33e2562125102024-03-21T00:26:20ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications2146-09572146-57032024-03-0114210.11121/ijocta.1468Some results regarding observability and initial state reconstruction for time-fractional systemsHamza Ben Brahim0Fatima-Zahrae El Alaoui1Khalid Zguaid2TSI Team, Faculty of Sciences, Moulay Ismail University, Meknes, MoroccoTSI Team, Faculty of Sciences, Moulay Ismail University, Meknes, MoroccoLRST Laboratory, The Higher School of Education and Training of Agadir (ESEFA), Ibn Zohr University, Agadir, Morocco The aim of this study is to present the notion of observability for a specific class of linear time-fractional systems of Riemann-Liouville type with a differentiation order between 1 and 2. To accomplish this goal, we first define the concept of observability and its features, then we extend the Hilbert Uniqueness Method (HUM) to determine the system's initial state. This method converts the reconstruction problem into a solvability one, leading to an algorithm that calculates the initial state. The effectiveness of the proposed algorithm is demonstrated through numerical simulations, which are presented in the final section. http://www.ijocta.org/index.php/files/article/view/1468Fractional calculusControl theoryTime-fractional systemsGlobal observabilityHUM approachNumerical approach |
| spellingShingle | Hamza Ben Brahim Fatima-Zahrae El Alaoui Khalid Zguaid Some results regarding observability and initial state reconstruction for time-fractional systems An International Journal of Optimization and Control: Theories & Applications Fractional calculus Control theory Time-fractional systems Global observability HUM approach Numerical approach |
| title | Some results regarding observability and initial state reconstruction for time-fractional systems |
| title_full | Some results regarding observability and initial state reconstruction for time-fractional systems |
| title_fullStr | Some results regarding observability and initial state reconstruction for time-fractional systems |
| title_full_unstemmed | Some results regarding observability and initial state reconstruction for time-fractional systems |
| title_short | Some results regarding observability and initial state reconstruction for time-fractional systems |
| title_sort | some results regarding observability and initial state reconstruction for time fractional systems |
| topic | Fractional calculus Control theory Time-fractional systems Global observability HUM approach Numerical approach |
| url | http://www.ijocta.org/index.php/files/article/view/1468 |
| work_keys_str_mv | AT hamzabenbrahim someresultsregardingobservabilityandinitialstatereconstructionfortimefractionalsystems AT fatimazahraeelalaoui someresultsregardingobservabilityandinitialstatereconstructionfortimefractionalsystems AT khalidzguaid someresultsregardingobservabilityandinitialstatereconstructionfortimefractionalsystems |