Adaptive synchronization of two different uncertain chaotic systems with unknown dead-zone input nonlinearities

The present work addresses chaos synchronization between two different general chaotic systems with parametric and structural uncertainties, subject to external disturbances and input dead-zone nonlinearities. In this regard, a novel robust controller has been designed that guarantees asymptotic stability of synchronization errors and boundedness of all closed-loop signals. One advantage of the proposed controller over the existing control algorithms is using only one update law for estimating the structural uncertainties, external disturbances, and unknown characteristics of the dead-zone nonlinearities, which reduces the computational burden considerably. The designed controller is singularity free, and a smooth projection algorithm has been used to make the controller more robust. In addition, a finite-time controller has been designed and its performance has been compared with the robustly designed controller.