Adaptive synchronization of chaotic systems with hysteresis quantizer input

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Chaos Theory

Background:

• Chaos synchronization is crucial for secure communication and complex system analysis.
• Input quantization in control systems can lead to chattering and performance degradation.
• Existing methods for quantized control often impose strict conditions on quantizer parameters.

Purpose of the Study:

• To develop new adaptive controller design methods for synchronizing uncertain nonlinear chaotic systems with input quantization.
• To address the limitations of existing control techniques regarding quantized parameters.
• To ensure the asymptotic stability and robustness of the proposed controllers.

Main Methods:

• Design of two novel adaptive robust control schemes.
• Utilizing hysteresis quantizers to avoid control signal chattering.
• Analytical verification of asymptotic stability for the proposed controllers.
• Application to chaotic gyroscope and Micro-Electro-Mechanical-System (MEMS) for validation.

Main Results:

• Successful chaos synchronization achieved for master-slave systems with unknown parameters and uncertainties.
• The proposed controllers do not require restrictive conditions on quantized parameters.
• Demonstrated avoidance of chattering phenomena through the use of hysteresis quantizers.
• Validated efficiency and robustness through practical applications.

Conclusions:

• The proposed adaptive controllers effectively achieve chaos synchronization in systems with input quantization.
• The novel design methods overcome limitations of previous approaches regarding parameter constraints.
• The controllers exhibit robustness and stability, validated by experimental applications.