Comparative Study of Neural Networks for Control of Nonlinear Dynamical Systems with Lyapunov Stability-Based Adaptive Learning Rates

Abstract

This paper performs the comparative study of two feed-forward neural networks: radial basis function network (RBFN), multilayer feed-forward neural network (MLFFNN) and a recurrent neural network: nonlinear auto-regressive with exogenous inputs (NARX) neural network for their ability to provide an adaptive control of nonlinear systems. Dynamic back-propagation algorithm is used to derive parameter update equations. To ensure stability and faster convergence, an adaptive learning rate is developed in the sense of discrete Lyapunov stability method. Both parameter variation and disturbance signal cases are considered for checking and comparing the robustness of controller. Three simulation examples are considered for carrying out this study. The results so obtained reveal that RBFN-based controller is performing better than that of NARX- and MLFFNN-based controllers.