Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode Control
Chaotic systems are always influenced by some uncertainties and external disturbances. This paper investigates the problem of practical synchronization of fractional-order chaotic systems with Gaussian fluctuation. A fractional integral (FI) sliding surface is proposed for synchronizing the uncertai...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/948782 |
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| _version_ | 1832566573049577472 |
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| author | Yong Xu Hua Wang |
| author_facet | Yong Xu Hua Wang |
| author_sort | Yong Xu |
| collection | DOAJ |
| description | Chaotic systems are always influenced by some uncertainties and external disturbances. This paper investigates the problem of practical synchronization of fractional-order chaotic systems with Gaussian fluctuation. A fractional integral (FI) sliding surface is proposed for synchronizing the uncertain fractional-order system, and then the sliding mode control technique is carried out to realize the synchronization of the given systems. One theorem about sliding mode controller is presented to prove that the proposed controller can make the system achieve synchronization. As a case study, the presented method is applied to the fractional-order Chen-Lü system, and simulation results show that the proposed control approach is capable to go against Gaussian noise well. |
| format | Article |
| id | doaj-art-cbd7d0da74054fcab40c580b02d39dce |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cbd7d0da74054fcab40c580b02d39dce2025-02-03T01:03:47ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/948782948782Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode ControlYong Xu0Hua Wang1Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, ChinaDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, ChinaChaotic systems are always influenced by some uncertainties and external disturbances. This paper investigates the problem of practical synchronization of fractional-order chaotic systems with Gaussian fluctuation. A fractional integral (FI) sliding surface is proposed for synchronizing the uncertain fractional-order system, and then the sliding mode control technique is carried out to realize the synchronization of the given systems. One theorem about sliding mode controller is presented to prove that the proposed controller can make the system achieve synchronization. As a case study, the presented method is applied to the fractional-order Chen-Lü system, and simulation results show that the proposed control approach is capable to go against Gaussian noise well.http://dx.doi.org/10.1155/2013/948782 |
| spellingShingle | Yong Xu Hua Wang Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode Control Abstract and Applied Analysis |
| title | Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode Control |
| title_full | Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode Control |
| title_fullStr | Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode Control |
| title_full_unstemmed | Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode Control |
| title_short | Synchronization of Fractional-Order Chaotic Systems with Gaussian Fluctuation by Sliding Mode Control |
| title_sort | synchronization of fractional order chaotic systems with gaussian fluctuation by sliding mode control |
| url | http://dx.doi.org/10.1155/2013/948782 |
| work_keys_str_mv | AT yongxu synchronizationoffractionalorderchaoticsystemswithgaussianfluctuationbyslidingmodecontrol AT huawang synchronizationoffractionalorderchaoticsystemswithgaussianfluctuationbyslidingmodecontrol |