Fault tolerant synchronisation of integer and fractional order 6D hyper-chaotic systems via two control signals

In this study, two 6D hyper-chaotic systems with integer and fractional orders in the presence of external disturbance and bounded parametric uncertainty with unknown bounds with two control signals are synchronised using an adaptive-sliding mode controller. In the definition of fractional order differentiation, Riemann-Louiville definition is used. To this end, the sliding surface and proper active feedback control law area determined and proper estimation laws are proposed for estimating unknown uncertainty bounds and the disturbance. The stability of the closed-loop control system is proved using the Lyapunov theorem. Simulation results in MATLAB demonstrate the desired efficiency of this method in the presence of disturbance and parametric uncertainty.