Robust Global Synchronization of a Hyperchaotic System with Wide Parameter Space via Integral Sliding Mode Control Technique

Abstract

The inherent property of invariance to structural and parametric uncertainties in sliding mode control makes it an attractive control strategy for chaotic dynamics control. This property can effectively constrain the chaotic property of sensitive dependence on initial conditions. In this paper, the trajectories of two identical four-dimensional hyperchaotic systems with fully-known parameters are globally synchronized using the integral sliding mode control technique. Based on the exponential reaching law and the Lyapunov stability principle, the problem of synchronizing the trajectories of the two systems was reduced to the control objective of asymptotically stabilizing the synchronization error state dynamics of the coupled systems in the sense of Lyapunov. To verify the effectiveness of the control laws, the model was numerically tested on a hyperchaotic system with a wide parameter space in a master-slave configuration. The parameters of the hyperchaotic system were subsequently varied to evolve a topologically non-equivalent hyperchaotic system that was identically coupled. In both cases, the modeled ISM control laws globally synchronized the dynamics of the coupled systems after transient times, which sufficiently proved the invariance property of the ISMC. This study offers an elegant technique for the modeling of an ISMC for hyperchaotic coupling systems. As an open problem, this synchronization technique holds promises for applications in robot motion control, chaos-based secure communication system design, and other sensitive nonlinear system control.