Adaptive Frequency-Based Constructive Wavelet Neural Network for Nonlinear Dynamic Systems

Neural networks (NNs) have gained significant popularity for modeling complex, nonlinear systems due to their powerful approximation capabilities. However, designing an appropriate network structure and tuning parameters remains challenging, especially for nonlinear dynamic systems where offline training data are unavailable and poor approximations from badly tuned NNs can cause instability. This article presents a novel adaptive frequency-based constructive wavelet NN (AFBCWNN) for tracking reference trajectories for a class of unknown nonlinear dynamic systems. Using online measurements, the AFBCWNN integrates adaptive weight updating, adjustable network structures, and rigorous stability analysis using Lyapunov techniques. Unlike conventional methods, the proposed AFBCWNN leverages frequency-domain analysis to estimate the energy distribution of the unknown nonlinear mapping from measured data. This frequency-based approach provides a uniform design guideline for network initialization, enabling the network to dynamically add wavelet bases when the desired accuracy is not achieved and prune nonenergy-active (low-energy) bases, reducing computational cost without compromising accuracy. Rigorous stability analysis establishes conditions for uniformly bounded trajectories, and simulation results confirm the AFBCWNN's superior performance in capturing complex, nonlinear dynamics compared to the existing adaptive methods.