Fractional order disturbance observer based adaptive sliding mode hybrid projective synchronization of fractional order Newton–Leipnik chaotic system

Abstract

This manuscript, presents the fractional order disturbances observer based adaptive sliding mode hybrid projective synchronization of commensurate and incommensurate fractional order Newton–Leipnik chaotic system with disturbance. Firstly, a fractional order disturbance observer (FODO) based on adaptive sliding mode control laws for a fractional order Newton–Leipnik system with unknown bounded disturbance is studied. The appropriate control gain parameters are chosen such that the disturbance observer can approximate the unknown disturbance well. Further, we design a simple sliding mode surface based on sliding mode control technique incorporating with the designed fractional order disturbance observer for developing a bounded hybrid projective synchronization control scheme. Numerical simulation results are given to demonstrate the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. To analyse the superiority of proposed methodology we have compared our results with earlier published results as well. Moreover, as an application, the proposed scheme is then applied to a secure communication system. Simulation results verify the proposed schemes success in the communication application.