Robust Synchronization Of Hyperchaotic Systems With Uncertainties And Its Application

Hyperchaotic system has two or more Lyapunov exponents, it has morecomplicated dynamic than chaotic system. Hyperchaos synchronization meansthat the trajectories of one of the systems will converge to the same values asthe other. The synchronization is structurally stable. Synchronization willpresents a variety of forms depending on the nature of the interacting systemsand the controlling scheme: complete synchronization, anti-synchronization,projective synchronization and so on. All of these forms have wideapplications. However, the systems are always influenced by kinds ofuncertainties such as external uncertainties, parameter perturbation andunknown parameters in practical applications which will affect thesynchronization between the two hyperchaotic system. It’s more significativeto study the robust synchronization of hyperchaotic systems.Firstly, this paper has research on anti-synchronization of hyperchaoticsystems with unknown parameters. Adaptive synchronization method aims atachieving synchronization between two hyperchaotic systems by usingadaptive control strategy to adjust some parameters. It’s suitable for thesynchronization between systems with unknown parameters. A adaptivecontroller is designed that can realize the anti-synchronization of thehyperchaotic system with unknown parameters based on this strategy. It’sproved that when the system is influenced by external uncertainties andparameter perturbation, the system is still robust. Then, it’s true that theadaptive synchronization method is effective, while its robustness remains tobe strengthen. Sliding mode control method has no relationship with externaluncertainties and uncertain parameters and it can guarantee the system hasstrong robustness. So the anti-synchronization of hyperchaotic systems withexternal uncertainties is studied by the combination of the active controlmethod and sliding mode control method. Numerical results are presented to justify that the systems which under the control of the proposed controlstrategy not only can achieve anti-synchronization but also has strongrobustness. While the application range of sliding mode control is limitedbecause of its chattering and both of the above two methods need complexmathematic calculation, so projective hyperchaotic synchronization is studiedbased on the state observer. The approach can judge whether the two systemscan achieve synchronization by calculating the rank of feedback matrix whichavoiding the complexity of calculating Lyapunov exponents. Especially theproblem of achieving hyperchaotic synchronization can convert into solvingthe linear inequality problem when there exists unknown parameters insystems that simplify the problem. Finally, the application of hyperchaoticsynchronization into secure communication is studied. A simulation study isperformed to verify that the security of secure communication is improved byusing the synchronization of hyperchaotic systems with uncertainties.