Synchronisation between two uncertain highly complex hyperchaotic systems in the occurrence of unmatched disturbances using disturbance observer-based adaptive SMC

In the literature of dynamical systems, many papers are seen on the synchronisation between chaotic/hyperchaotic systems. In these reported works, the synchronisation is done when the external disturbances are added to state of the slave system where controller is added, i.e. using matched disturbances. Occasional work is reported on the synchronisation between uncertain hyperchaotic systems in the presence of unmatched. In this paper, the synchronisation concept between two unidentically operated initial conditions highly complex hyperchaotic systems is shown by treating them as the master/transmitter and the slave/receiver systems. The synchronisation is achieved in the presence of added disturbance in the slave system, where controller is not inserted and also considering unidentified gains of the switching mode control law of the SMC. A nonlinear disturbance estimator-based adaptive sliding mode control (SMC) is proposed to realise the synchronisation. The MATLAB simulation results confirm that the synchronisation strategy is worked successfully, and the proposed works are validated.