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Adaptive complete synchronization of chaotic dynamical network with unknown and mismatched parameters
Yuzhu Xiao1, Wei Xu, Xiuchun Li
1Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China. yuzhuxiao@mail.nwpu.edu.cn
Chaos (Woodbury, N.Y.)
|October 2, 2007
Summary
This study introduces an adaptive controller for synchronizing chaotic dynamical networks with unknown parameters. The proposed control scheme proves effective and robust, even in the presence of noise.
Area of Science:
- Chaos theory
- Nonlinear dynamics
- Control systems
Background:
- Chaotic dynamical networks exhibit complex behaviors.
- Synchronization of chaotic systems is crucial for various applications.
- Parameter uncertainties and mismatches pose significant challenges in control design.
Purpose of the Study:
- To design an adaptive controller for achieving asymptotic synchronization of chaotic dynamical networks.
- To address systems with unknown and mismatched parameters.
- To establish generic sufficient conditions for synchronization.
Main Methods:
- Utilizing the invariance principle of differential equations for controller design.
- Developing an adaptive control strategy.
- Employing numerical simulations to validate the proposed method.
Main Results:
- The proposed adaptive controller effectively synchronizes chaotic dynamical networks.
- Generic sufficient conditions for asymptotic synchronization were derived.
- The control scheme demonstrated robustness against weak noise.
Conclusions:
- The developed adaptive controller is effective for synchronizing chaotic dynamical networks with uncertainties.
- The invariance principle provides a solid foundation for designing robust synchronization controllers.
- Numerical simulations confirm the practical applicability and resilience of the proposed method.
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