Control and synchronization of the generalized Lorenz system with mismatched uncertainties using backstepping technique and time-delay estimation

Abstract

We propose a robust control technique for regulation and synchronization of the generalized Lorenz system (GLS) that covers the Lorenz system, Chen system and Lü system. The proposed control provides synergy through the combination of the backstepping control and time-delay estimation (TDE) technique. TDE is used to estimate and cancel nonlinearities and uncertainties while the backstepping method is adopted to provide robustness against matched and mismatched uncertainties. As a result, we observe in numerical simulation that the proposed technique shows better performances in regulating and synchronizing the GLS with mismatched uncertainties, in comparison with existing schemes. The efficacy of the proposed technique is also validated with a circuit-implemented chaotic system. © 2017 John Wiley & Sons, Ltd.