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