Adaptive backstepping Elman-based neural control for unknown nonlinear systems

This paper proposes an Elman-based self-organizing RBF neural network (ESRNN) which is a recurrent multilayered neural network, thus the ESRNN can handle the dynamic response. The ESRNN starts without any hidden neurons and all the hidden neurons are generated and learning online through a simultaneous structure and parameter learning via the Mahalanobis distance approach. Furthermore, an adaptive backstepping Elman-based neural control (ABENC) system which is composed of a computation controller and a switching controller is proposed. In this approach, the ESRNN is used to online approximate the unknown nonlinear system dynamics based on a Lyapunov function, so that system stability can be guaranteed. The switching controller is designed to eliminate the effect of the approximation error introduced by the ESRNN upon system stability. Finally, to effectively demonstrate the effectiveness of the proposed ABENC scheme, a chaotic system and an inverted pendulum are applied as example studies. The simulation results demonstrate that the proposed ABENC system can achieve favorable control performance after the structure and parameter learning of the ESRNN.