Synchronization of a Class of Nonlinear Systems With and Without Uncertainty Using State Feedback and Extended Kalman Filter Based Control Scheme

The paper elaborates on various synchronization aspects for nonlinear systems belonging to a specific class, under different scenarios. The method proposed in the article refers to the Lyapunov direct method and Extended Kalman Filter technique to ensure the convergence of the slave state trajectories to the corresponding master state trajectories. Initially, an output feedback-based synchronization approach is attempted, assuming that bounds of unmeasurable states are available for controller synthesis. However, this approach has limitations in handling complete parametric uncertainty for the considered class of systems. To overcome this limitation, a state feedback-based synchronization scheme is presented, and an appropriate state feedback controller and parametric adaptation laws are designed analytically. In the case where only output states are accessible for feedback, and the system is subjected to complete parametric uncertainty, an Extended Kalman Filter based estimation scheme is used. This approach facilitates achieving synchronization despite the presence of external channel noise disturbances with a Gaussian distribution. The potency of the proposed results is successfully substantiated for the chaotic Lorenz system, which belongs to the considered class of nonlinear systems. Ultimately, numerical simulations are provided to corroborate the efficacy of proposed synchronization and estimation strategy.