Adaptive Hybrid Function Projective Synchronization of Chaotic Systems with Time-Varying Parameters
The adaptive hybrid function projective synchronization (AHFPS) of different chaotic systems with unknown time-varying parameters is investigated. Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make...
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| Veröffentlicht in: | Mathematical Problems in Engineering 2012-01, Vol.2012 (2012), p.95-112-407 |
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| container_end_page | 112-407 |
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| container_title | Mathematical Problems in Engineering |
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| creator | Xing, Jinsheng |
| description | The adaptive hybrid function projective synchronization (AHFPS) of different chaotic systems with unknown time-varying parameters is investigated. Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time-varying parameters are bounded by the product of a known function of t and an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage-like adaptation law is also proposed to guarantee the ultimately uni-formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. Moreover, numerical simulation results are presented to verify the effectiveness of the proposed scheme. |
| doi_str_mv | 10.1155/2012/619708 |
| format | Article |
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Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time-varying parameters are bounded by the product of a known function of t and an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage-like adaptation law is also proposed to guarantee the ultimately uni-formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. Moreover, numerical simulation results are presented to verify the effectiveness of the proposed scheme.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2012/619708</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Limiteds</publisher><subject>Adaptive control ; Adaptive control systems ; Adaptive systems ; Chaos theory ; Chemical reactors ; Communication ; Control stability ; Control theory ; Economic models ; Engineering ; Hybrid systems ; Law ; Lorenz system ; Mathematical analysis ; Mathematical models ; Neural networks ; Parameter modification ; Parameter robustness ; Robust control ; Studies ; Synchronism ; Synchronization ; Time synchronization</subject><ispartof>Mathematical Problems in Engineering, 2012-01, Vol.2012 (2012), p.95-112-407</ispartof><rights>Copyright © 2012 Jinsheng Xing.</rights><rights>Copyright © 2012 Jinsheng Xing. Jinsheng Xing et al. 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Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time-varying parameters are bounded by the product of a known function of t and an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage-like adaptation law is also proposed to guarantee the ultimately uni-formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. 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Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time-varying parameters are bounded by the product of a known function of t and an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage-like adaptation law is also proposed to guarantee the ultimately uni-formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. 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| subjects | Adaptive control Adaptive control systems Adaptive systems Chaos theory Chemical reactors Communication Control stability Control theory Economic models Engineering Hybrid systems Law Lorenz system Mathematical analysis Mathematical models Neural networks Parameter modification Parameter robustness Robust control Studies Synchronism Synchronization Time synchronization |
| title | Adaptive Hybrid Function Projective Synchronization of Chaotic Systems with Time-Varying Parameters |
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