Approximation of dynamic system by recurrent neural network

Aim To study the approximating capacity of a new locally recurrent neural network, and draw much more general conclusions about the non-autonomous system approximation. Methods A new locally recurrent neural network model was explored, the approximation results were drawn by using the basic neural approximating theorem and other mathematics analyzing theory. Results Simulation results showed the approximation results were correct and the recurrent neural network was powerful for the nonlinear dynamic system approximation. Conclusion It is proved that the finite time trajectories of a given n-dimensional nonlinear dynamic system with a control input can be approximated by the states of the locally recurrent network under the condition of the same input and approximate initial states.