Adaptive Hybrid Synchronization of Lorenz-84 System with Uncertain Parameters

Abstract

This paper presents the adaptive control and hybrid synchronization of Lorenz-84 chaotic system using a master-slave topology. The Lorenz-84 is an 11-term dissipative system that possessed  four quadratic nonlinearities in its coupled algebraic structure which results to the evolution of  a dense chaotic attractors in both 2-D and 3-D spaces. Firstly, an adaptive nonlinear feedback controller was designed to suppress the chaotic dynamics of the system. By using Lyapunov stability criterion, the asymptotic stability of the error states was guaranteed and the state dynamics were stabilized. Secondly, adaptive nonlinear feedback controllers were designed to guarantee the co-existence of synchronization and anti-synchronization of the system. By suitable selection of feedback coefficients and Lyapunov function candidate, the uncertain parameters of the slave system were estimated. Numerical simulations via MATLAB show the convergence of the uncertain parameters to their true values after a transient time while the two systems synchronized completely.