Synchronization of Fractional-Order Chaotic Systems in the Presence of Order Uncertainty Using Projection Recurrent Neural Network based Sliding Mode Control

In this paper, the synchronization of fractional-order chaotic Lorenz and Chen systems using a constrained optimal control approach has been investigated.The control algorithm consists of two operative loops where the instant estimation of fractional order using a numerical optimizer is carried out through the inner loop, while the control laws are generated using sliding mode control principal based on exponential reaching conditions.The proposed method to estimate the fractional order is based on forming linear regression for the fractional order equations of the Lorenz and Chen systems.The proposed algorithm has high performance in the presence of fractional order uncertainty in comparison with robust control approaches.