Pragmatical adaptive synchronization of different orders chaotic systems with all uncertain parameters via nonlinear control

A new adaptive synchronization scheme by pragmatical asymptotically stability theorem is proposed in this paper. Based on this theorem and nonlinear control theory, a new adaptive synchronization scheme to design controllers can be obtained and especially the constraints for minimum values of feedback gain K in controllers can be derived. This new strategy shows that the constraint values of feedback gain K are related to the error of unknown and estimated parameters if the goal system is given. Through this new strategy, an appropriate feedback gain K can be always decided easily to obtain controllers achieving adaptive synchronization. Two identical Lorenz systems with different initial conditions and two completely different nonlinear systems with different orders, augmented Rossler's system and Mathieu-van der Pol system, are used for illustrations to demonstrate the efficiency and effectiveness of the new adaptive scheme in numerical simulation results.