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

摘要

Adaptive controllers are designed to synchronize two different chaoticsystems with uncertainties, including unknown parameters, internal and externalperturbations. Lyapunov stability theory is applied to prove that under someconditions the drive-response systems can achieve synchronization with uniformultimate bound even though the bounds of uncertainties are not known exactly inadvance. The designed controllers contain only feedback terms and partialnonlinear terms of the systems, and they are easy to implement in practice. TheLorenz system and Chen system are chosen as the illustrative example to verifythe validity of the proposed method. Simulation results also show that thepresent control has good robustness against different kinds of disturbances.