Adaptive Design of Controller and Synchronizer for Lu-Xiao Chaotic System with Unknown Parameters

This paper establishes new results for the adaptive design of controller and synchronizer for the Lu-Xiaochaotic system (2012) with unknown parameters.First part of this paper involves the design of adaptivecontroller for the Lu-Xiao chaotic system to stabilize to its unstable equilibrium at the origin. The adaptivecontroller design is carried out using Lyapunov stability theory and adaptive control theory. The secondpart of thispaper involves the design of adaptive synchronizer for identical Lu-Xiao chaotic systems withunknown parameters. The adaptive synchronizer design is carried out using Lyapunov stability theory andadaptive control theory. Numerical simulations using MATLAB have been shown to depict and validate theadaptive design of controller and synchronizer for the Lu-Xiao chaotic system with unknown parameters