Robust synchronization with uniform ultimate bound between two different chaotic systems with uncertainties

TL;DR

This paper presents an adaptive control method to synchronize two different chaotic systems with uncertainties, ensuring a uniform ultimate bound despite unknown bounds and disturbances, demonstrated on Lorenz and Chen systems.

Contribution

It introduces a robust adaptive synchronization approach that handles uncertainties without requiring exact bounds, using simple feedback and nonlinear terms.

Findings

Achieves synchronization with uniform ultimate bound despite uncertainties

Demonstrates robustness against disturbances through simulations

Applicable to systems like Lorenz and Chen chaotic models

Abstract

Adaptive controllers are designed to synchronize two different chaotic systems with uncertainties, including unknown parameters, internal and external perturbations. Lyapunov stability theory is applied to prove that under some conditions the drive-response systems can achieve synchronization with uniform ultimate bound even though the bounds of uncertainties are not known exactly in advance. The designed controllers contain only feedback terms and partial nonlinear terms of the systems, and they are easy to implement in practice. The Lorenz system and Chen system are chosen as the illustrative example to verify the validity of the proposed method. Simulation results also show that the present control has good robustness against different kinds of disturbances.