Adaptive robust synchronization of fractional order nonlinear chaotic systems with input delay

In this paper, predictor based synchronization of input delay fractional order nonlinear chaotic systems in the presence of disturbance has been investigated. Firstly, a novel sliding mode controller is presented for delay‐free fractional order systems which ensures chaos synchronization exponentially in an arbitrary time. To ensure the effectiveness of the proposed controller, the arbitrary time convergence of both sliding and reaching phases has been investigated and proven. The presented scheme is completely novel in the sense that the convergence rate can be adjusted in addition to the convergence time. Secondly, an exponential arbitrary time disturbance observer is designed for delay fractional systems to estimate the external disturbance with an exponential rate. The proposed observer can ensure zero estimation error in a user‐defined time independent of initial conditions. Then, by incorporating the disturbance observer, a robust prediction based sliding mode synchronization method is designed for delay systems in the presence of disturbances. Finally, an upper bound for the input delay is determined and it is shown that for a delay less than this value, the synchronization error will be bounded. The effectiveness of the proposed method is validated via numerical simulations. It is noteworthy that this is the first study to propose predictor based control for input delay fractional order nonlinear systems.