Adaptive Nonlinear Controller Design for Robust Synchronization of Chaotic Systems in the Presence of Actuator Aaturation

The analytic approach proposed in this paper is synchronization of chaotic systems in the presence of practical constraints. Constraints that this paper is considered on the study of synchronization are: actuator saturation, presence of external disturbances and model uncertainties. The synchronization happens between the two nonlinear master and slave systems. Control law is designed in such a way that the state variables of the slave system follow the state variables of the master system in the presence of uncertainty and external disturbances and by considering the actuator saturation constraint. Therefore, based on the error model, sliding surface, robust control law and adaptive laws are designed in a way that robust synchronization occurs. For this purpose, a theorem is proposed and according to the Lyapunov approach it is proved that the synchronization error despite the uncertainty terms reaches zero by actuator saturation constraint. In order to show the practical performance of proposed approach, the aforesaid method is based on practical system of gyros that chaotic behavior is implemented and the computer simulations show proper performance of the proposed law in robust synchronization of aforesaid practical system.