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.

Sliding Mode Control Design for Magnetic Levitation System

“…The sliding mode control is a robust nonlinear controller which can easily handle a system's nonlinearity, uncertainty and model mismatch [49]- [52]. It has been implemented to control both linear and nonlinear systems: hydraulic [53][54], single machine infinite bus system [55], inverted pendulum [56]- [58], DC motor [59], induction motor [60], suspension [61], permanent magnet synchronous generator [62], hyperchaotic system [63], quadcopter [64], mobile robot [65][66], stepper motor [67], tank system [68] and robot manipulator [69]. According to study findings, SMC has been reported to give promising results.…”

Finite-Time Synchronization of the Rabinovich and Rabinovich-Fabrikant Chaotic Systems for Different Evolvable Parameters

“…Among the intriguing phenomena associated with chaotic systems is synchronization, where the dynamics of two chaotic systems, whether identical or non-identical, are coupled through appropriate control laws within finite time. Numerous synchronization schemes have been developed to facilitate this coupling, including adaptive control-based synchronization [18], adaptive hybrid synchronization [19], functional projective synchronization [20], and sliding mode control-based synchronization [21], [22], fuzzy synchronization [23], invariant ellipsoids method [24]. Each scheme serves specific purposes in different contexts and applications.…”