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Published on: May 8, 2021
Generalized synchronization with uncertain parameters of nonlinear dynamic system via adaptive control
Cheng-Hsiung Yang1, Cheng-Lin Wu1
1Graduate Institute of Automation and Control, National Taiwan University of Science and Technology, No. 43, Section 4, Keelung Road, Taipei 106, Taiwan.
This study introduces an adaptive control scheme for generalized adaptive chaos synchronization, enabling synchronization of chaotic systems even with unknown parameters. The method ensures reliable synchronization for uncertain chaotic systems.
Area of Science:
- Nonlinear Dynamics
- Control Theory
- Chaos Theory
Background:
- Chaos synchronization is crucial for secure communication and complex system analysis.
- Existing methods often require precise knowledge of system parameters.
- Uncertainty in chaotic parameters poses a significant challenge for synchronization.
Purpose of the Study:
- To develop a generalized adaptive control scheme for chaos synchronization.
- To address synchronization in the presence of uncertain chaotic parameters.
- To demonstrate the effectiveness of the proposed method on new Lorenz-Stenflo systems.
Main Methods:
- Design of a generalized adaptive chaos synchronization controller.
- Application of Lyapunov stability theory for controller design.
- Derivation of adaptive controller update laws for uncertain parameters.
Main Results:
- An analytic expression for the adaptive controller and its update laws was derived.
- The proposed method successfully achieved generalized adaptive chaos synchronization.
- Effectiveness was verified through numerical simulations on new Lorenz-Stenflo systems.
Conclusions:
- The developed adaptive control scheme effectively achieves generalized chaos synchronization with uncertain parameters.
- The method provides a robust approach for synchronizing chaotic systems under parameter uncertainty.
- Numerical simulations confirm the validity and efficiency of the proposed synchronization technique.
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