Fault-tolerant complete synchronization of integer and fractional derivative 6D hyper-chaotic systems with unknown time delay

Abstract

In this study, synchronization of two 6D hyper-chaotic systems in the presence of bounded disturbance and uncertainty with unknown bounds and time delay for integer-order and fractional-order systems is investigated. In the first step of the selected control approach, a proper sliding surface is defined for synchronization of two hyper-chaotic systems, a proper active control is considered, and proper adaptive laws are used to estimate the uncertainty bounds, the unknown disturbance, and unknown time delay of the master and slave systems. The stability of the closed-loop control system is proved using the Lyapunov theorem. Simulation results using MATLAB verify desired performance of the proposed controllers in the presence of unknown disturbance, uncertainty, and time delay.