Adaptive Control Design for Arneodo Chaotic System with Uncertain Parameters and Input Saturation

Abstract

In this paper, tracking controller and synchronization controller of the Arneodo chaotic system with uncertain parameters and input saturation are considered. An adaptive tracking control law and an adaptive synchronization control law are proposed based on backstepping and Lyapunov stability theory. The adaptive laws of the unknown parameters are derived by using the Lyapunov stability theory. To handle the effect caused by the input saturation, an auxiliary system is used to compensate the tracking error and synchronization error. The proposed adaptive tracking control and synchronization schemes ensure the effects of tracking and synchronization. Several examples have been detailed to illuminate the design procedure.

A General Criterion for Unidirectionally Coupled Generalized Chaotic Synchronization with a Desired Manifold

“…Lerescu et al [23] and Guo and Li [24] used OPCL control and adaptive feedback control to synchronize two identical systems from Sprott's simplest chaotic system set. Cheng et al [25] proposed an adaptive synchronization control law for the Arneodo chaotic system with uncertain parameters and input saturation, and an auxiliary system is used to compensate the synchronization error. Tamba et al [26] applied the adaptive control to obtain the synchronization of the system with an absolute nonlinearity.…”