Nonlinear dynamical system approximation and adaptive control based on hybrid-feed-forward recurrent neural network: Simulation and stability analysis

We proposed an online identification and adaptive control framework for the nonlinear dynamical systems using a novel hybrid-feed-forward recurrent neural network (HFRNN) model. The HFRNN is a combination of a feed-forward neural network (FFNN) and a local recurrent neural network (LRNN). We aim to leverage the simplicity of FFNN and the effectiveness of RNN to capture changing dynamics accurately and design an indirect adaptive control scheme. To derive the weights update equations, we have applied the gradient-descent-based Back-Propagation (BP) technique, and the stability of the proposed learning strategy is proven using the Lyapunov stability principles. We also compared the proposed method's results with those of the Jordan network-based controller (JNC) and the local recurrent network-based controller (LRNC) in the simulation examples. The results demonstrate that our approach performs satisfactorily, even in the presence of disturbance signals.