Abstract: For the purpose of solving the problems in identification and modeling of nonlinear dynamic system using recurrent neural networks (RNN), a nonlinear state space model is investigated for RNN. The convergence criterion for networks training is discussed under minimum mean square error (MMSE). The stochastic variable in the Kalman filter formulations is researched. A parameter-augmented nonlinear state space equation for RNN is proposed. A derivative-free Kalman filter is employed to estimate the augmented parameters and to update weights of RNN by using artificial white noise to compel RNN to learn. Compared with the extended Kalman filter (EKF), computation of Jacobian information is avoided and the problem of slow convergence rate of algorithm based on gradient learning is also solved. The application of RNN in the identification and modeling of an electro-hydraulic servo system shows that RNN is capable of tracking the dynamic pressure of the hydraulic cylinder. The new algorithm has faster convergence and higher precision compared to the algorithm of extended Kalman filter.

Key words: Electro-hydraulic servo system, Kalman filter, Nonlinear state space, System identification