Adaptive Chaos Synchronization Based on the Iterated Extended Kalman Filtering Trained Radial Basis Function Neural Networks

Based on the iterated extended Kalman filtering trained radial basis function neural networks, this contribution investigates the adaptive synchronization problem between different chaotic systems in presence of unknown system parameters, with random noises to the observed outputs and without needing to estimate the system parameters. The input vector to the radial basis function neural network is composed of the controlled responsive system’s delayed signal with given length, and the nonlinear filtering model is established by using the prototype and weight of the radial basis function neural network as state equation and the output of the radial basis function neural network to present the observation equation. So the state transition matrix is an identity matrix, and the observed estimation value of the nonlinear filtering is the output value of the controlled response system. Finally, the synchronizations between Lorenz system and Rössler system, hyperchaotic Chen system and hyperchaotic Lü system are taken as two illustrative examples to demonstrate the effectiveness of the proposed method, and the simulation results verify the iterated extended Kalman filtering trained radial basis function neural network’s success in the adaptive chaos synchronization.