Online-Optimized Gated Radial Basis Function Neural Network-Based Adaptive Control

Real-time adaptive control of nonlinear systems with unknown dynamics and time-varying disturbances demands precise modeling and robust parameter adaptation. While existing neural network-based strategies struggle with computational inefficiency or inadequate temporal dependencies, this study proposes a hybrid control framework integrating a Temporal-Gated Radial Basis Function (TGRBF) network with a nonlinear robust controller. The TGRBF synergizes radial basis function neural networks (RBFNNs) and gated recurrent units (GRUs) through dynamic gating, enabling efficient offline system identification and online temporal modeling with minimal parameter overhead (14.5% increase vs. RBFNNs). During control execution, an event-triggered optimization mechanism activates momentum-explicit gradient descent to refine network parameters, leveraging historical data to suppress overfitting while maintaining real-time feasibility. Concurrently, the nonlinear controller adaptively tunes its gains via Jacobian-driven rules derived from the TGRBF model, ensuring rapid error convergence and disturbance rejection. Lyapunov-based analysis rigorously guarantees uniform ultimate boundedness of both tracking errors and adaptive parameters. Simulations on a nonlinear benchmark system demonstrate the framework's superiority: compared to PID and fixed-gain robust controllers, the proposed method reduces settling time by 14.2%, limits overshoot to 10%, and achieves 48.4% lower integral time-weighted absolute error under dynamic disturbances. By unifying data-driven adaptability with stability-guaranteed control, this work advances real-time performance in partially observable, time-varying industrial systems.