Fractional order disturbance observer based adaptive sliding mode synchronization of commensurate fractional order Genesio-Tesi system

In this manuscript, we have studied the adaptive sliding mode synchronization of commensurate fractional order Genesio-Tesi system with disturbance. Firstly, we have discussed the fractional order disturbance observer (FODO) which is based on adaptive sliding mode control laws for a commensurate fractional order Genesio-Tesi system with unknown bounded disturbance. Appropriate control gain parameters have been chosen in such a manner, so that the disturbance observer can approximate the unknown disturbance well. Further, we have designed a simple sliding mode surface based on sliding mode control technique, incorporating the designed fractional order disturbance observer for developing a bounded synchronization control scheme. Finally, the viability and the efficacy of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance for fractional order Genesio-Tesi system is established by the numerical simulation results. We have observed that for different parameters and fractional orders of Genesio-Tesi system the synchronization time varies, which is also demonstrated in numerical simulations. To visualize the robustness and effectiveness 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 scheme. Simulation results verify the proposed schemes success in the communication application.