Adaptive single input sliding mode control for hybrid-synchronization of uncertain hyperchaotic Lu systems

This paper addresses the problem of hybrid synchronization for hyperchaotic Lu systems without and with uncertain parameters via a single input sliding mode controller (SMC). Based on the SMC approach, the proposed controller not only minimizes the influence of uncertainty but also enhances the robustness of the system. The uncertain parameters are estimated by using new adaptation laws which ensure the uncertain parameters convergence to their original value. A hybrid synchronization scheme is useful to maintain the vastly secured and secrecy in the area of secure communication by using the control theory approach. The proposed hybrid synchronization results are providing a superiority of forming a chaotic secure communication scheme. Finally, a numerical example is provided to demonstrate the validity of the theoretical analysis.