Synchronized Dynamics of Hyperchaotic Flows via an Improved Finite-Time Adaptive Controller Design

Abstract

We proposed a performance-improved finite-time adaptive synchronizing controllers and parameter update laws for coupling the dynamics of identical 4D hyperchaotic flows. The four-dimensional hyperchaotic flows consists of 12 terms and 11 system parameters and possessed very rich dynamics and larger parameter space. The performance of the proposed finite-time adaptive synchronizing controller was enhanced by the introduction of scalar quantities known as global controller strength coefficients and parameter update strength coefficients respectively, into the algebraically-derived control and parameter update structures, in order to constrained overshoots of the trajectories of the coupled systems and accelerate their rate of uniform convergence in finite time. Numerical simulation results obtained confirmed that the uniform asymptotic convergence rate of the coupling trajectories was faster, while the parameter update laws give a stable identification of the unknown system parameters in a global synchronizing time. A comparative analysis of the convergence time of the proposed adaptive controllers with recently published works indicated that the proposed controller has faster rates of uniform convergence of system trajectories.