Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros
This paper considers the finite-time synchronization of chaotic systems in the presence of model uncertainties and/or external disturbances. The synchronization happens between the two nonlinear master and slave systems. Control law is designed in such a way that the state variables of the slave sys...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2018-01-01
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| Series: | Systems Science & Control Engineering |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/21642583.2018.1428695 |
| _version_ | 1818510325591310336 |
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| author | Sammaneh Mohammadpour Tahereh Binazadeh |
| author_facet | Sammaneh Mohammadpour Tahereh Binazadeh |
| author_sort | Sammaneh Mohammadpour |
| collection | DOAJ |
| description | This paper considers the finite-time synchronization of chaotic systems in the presence of model uncertainties and/or external disturbances. The synchronization happens between the two nonlinear master and slave systems. Control law is designed in such a way that the state variables of the slave system follow the state variables of the master system in the presence of uncertainties and external disturbances. In order to design a robust finite-time controller, first, a novel terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then a terminal sliding mode controller is designed which can conquer the uncertainties and guarantees the finite-time stability of the sliding motion equations. In this regard, a theorem is proposed and according to the Lyapunov approach it is proved that the synchronization happenes in finite-time. Additionally, in order to show the applicability of the proposed controller, it is applied on two practical systems, the Duffing–Holmes system and chaotic gyroscope system. Computer simulations verify the theoretical results and also display the effective performance of the proposed controller. |
| first_indexed | 2024-12-10T22:57:40Z |
| format | Article |
| id | doaj.art-8d1618c5d58347bdb402605250b9017c |
| institution | Directory Open Access Journal |
| issn | 2164-2583 |
| language | English |
| last_indexed | 2024-12-10T22:57:40Z |
| publishDate | 2018-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Systems Science & Control Engineering |
| spelling | doaj.art-8d1618c5d58347bdb402605250b9017c2022-12-22T01:30:14ZengTaylor & Francis GroupSystems Science & Control Engineering2164-25832018-01-0161283610.1080/21642583.2018.14286951428695Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyrosSammaneh Mohammadpour0Tahereh Binazadeh1Shiraz University of TechnologyShiraz University of TechnologyThis paper considers the finite-time synchronization of chaotic systems in the presence of model uncertainties and/or external disturbances. The synchronization happens between the two nonlinear master and slave systems. Control law is designed in such a way that the state variables of the slave system follow the state variables of the master system in the presence of uncertainties and external disturbances. In order to design a robust finite-time controller, first, a novel terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then a terminal sliding mode controller is designed which can conquer the uncertainties and guarantees the finite-time stability of the sliding motion equations. In this regard, a theorem is proposed and according to the Lyapunov approach it is proved that the synchronization happenes in finite-time. Additionally, in order to show the applicability of the proposed controller, it is applied on two practical systems, the Duffing–Holmes system and chaotic gyroscope system. Computer simulations verify the theoretical results and also display the effective performance of the proposed controller.http://dx.doi.org/10.1080/21642583.2018.1428695Chaotic systemsfinite-time controlrobust synchronizationterminal sliding modeLyapunov stability |
| spellingShingle | Sammaneh Mohammadpour Tahereh Binazadeh Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros Systems Science & Control Engineering Chaotic systems finite-time control robust synchronization terminal sliding mode Lyapunov stability |
| title | Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros |
| title_full | Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros |
| title_fullStr | Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros |
| title_full_unstemmed | Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros |
| title_short | Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros |
| title_sort | robust finite time synchronization of uncertain chaotic systems application on duffing holmes system and chaos gyros |
| topic | Chaotic systems finite-time control robust synchronization terminal sliding mode Lyapunov stability |
| url | http://dx.doi.org/10.1080/21642583.2018.1428695 |
| work_keys_str_mv | AT sammanehmohammadpour robustfinitetimesynchronizationofuncertainchaoticsystemsapplicationonduffingholmessystemandchaosgyros AT taherehbinazadeh robustfinitetimesynchronizationofuncertainchaoticsystemsapplicationonduffingholmessystemandchaosgyros |