Adaptive, Observer-Based Synchronization of Different Chaotic Systems
In this study, the problem of master–slave synchronization of two different chaotic systems is considered and solved under a novel set of assumptions. The mathematical model of each of them contains unknown, constant parameters. Only a single output of the master system is available, and only a sing...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/7/3394 |
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| author | Jacek Kabziński Przemysław Mosiołek |
| author_facet | Jacek Kabziński Przemysław Mosiołek |
| author_sort | Jacek Kabziński |
| collection | DOAJ |
| description | In this study, the problem of master–slave synchronization of two different chaotic systems is considered and solved under a novel set of assumptions. The mathematical model of each of them contains unknown, constant parameters. Only a single output of the master system is available, and only a single input of the slave system is a control input. The proposed, novel approach is based on the active cooperation of the adaptive observer of the master system and adaptive controller of the slave. The tuning function technique is included in the observer–controller design to avoid overparameterization. Complexity explosion and unacceptable increases in adaptive parameters are prevented by proper adaptive techniques application. Due to the selected observer type, the derivation is restricted to the defined class of master systems—output-nonlinear parametric (ONP) systems. Linear transformation of several popular chaotic systems (e.g., Arneodo, Arneodo–Coullet, Genesio–Tesi, Lur’e) into the ONP form is discussed. The stability of the whole, closed-loop system is derived using Lyapunov techniques and examples of implementation (synchronization of Arneodo and 3D jerk systems) are provided. |
| first_indexed | 2024-03-09T12:08:22Z |
| format | Article |
| id | doaj.art-23d7fca724d4445f889cd8f494c4cefb |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T12:08:22Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-23d7fca724d4445f889cd8f494c4cefb2023-11-30T22:55:07ZengMDPI AGApplied Sciences2076-34172022-03-01127339410.3390/app12073394Adaptive, Observer-Based Synchronization of Different Chaotic SystemsJacek Kabziński0Przemysław Mosiołek1Institute of Automatic Control, Lodz University of Technology, Stefanowskiego 18, 90-537 Lodz, PolandInstitute of Automatic Control, Lodz University of Technology, Stefanowskiego 18, 90-537 Lodz, PolandIn this study, the problem of master–slave synchronization of two different chaotic systems is considered and solved under a novel set of assumptions. The mathematical model of each of them contains unknown, constant parameters. Only a single output of the master system is available, and only a single input of the slave system is a control input. The proposed, novel approach is based on the active cooperation of the adaptive observer of the master system and adaptive controller of the slave. The tuning function technique is included in the observer–controller design to avoid overparameterization. Complexity explosion and unacceptable increases in adaptive parameters are prevented by proper adaptive techniques application. Due to the selected observer type, the derivation is restricted to the defined class of master systems—output-nonlinear parametric (ONP) systems. Linear transformation of several popular chaotic systems (e.g., Arneodo, Arneodo–Coullet, Genesio–Tesi, Lur’e) into the ONP form is discussed. The stability of the whole, closed-loop system is derived using Lyapunov techniques and examples of implementation (synchronization of Arneodo and 3D jerk systems) are provided.https://www.mdpi.com/2076-3417/12/7/3394adaptive backsteppingchaos synchronizationnonlinear observer |
| spellingShingle | Jacek Kabziński Przemysław Mosiołek Adaptive, Observer-Based Synchronization of Different Chaotic Systems Applied Sciences adaptive backstepping chaos synchronization nonlinear observer |
| title | Adaptive, Observer-Based Synchronization of Different Chaotic Systems |
| title_full | Adaptive, Observer-Based Synchronization of Different Chaotic Systems |
| title_fullStr | Adaptive, Observer-Based Synchronization of Different Chaotic Systems |
| title_full_unstemmed | Adaptive, Observer-Based Synchronization of Different Chaotic Systems |
| title_short | Adaptive, Observer-Based Synchronization of Different Chaotic Systems |
| title_sort | adaptive observer based synchronization of different chaotic systems |
| topic | adaptive backstepping chaos synchronization nonlinear observer |
| url | https://www.mdpi.com/2076-3417/12/7/3394 |
| work_keys_str_mv | AT jacekkabzinski adaptiveobserverbasedsynchronizationofdifferentchaoticsystems AT przemysławmosiołek adaptiveobserverbasedsynchronizationofdifferentchaoticsystems |