A Lyapunov-derived network parameters adjustment for indirect neural adaptive control: real-time application on a chemical reactor

This paper presents a Hybrid Parameter Adaptation Strategy (HPAS) for neural adaptive control of nonlinear systems using a Recurrent Neural Network (RNN). Unlike existing Lyapunov-based adaptive neural controllers, which typically rely on fixed or heuristic learning rates, HPAS integrates RTRL-based weight adaptation with a Lyapunov-derived adaptive learning rate (NARA). This allows the learning rate to adjust dynamically in real time while guaranteeing closed-loop stability. Two variants of NARA are proposed. Global-error-based (NARAGE) targets overall system performance, while tracking-error-based (NARACE) focuses on precise trajectory tracking. Theoretical analysis rigorously establishes the stability guarantees of the proposed approach. The strategy is validated experimentally on a chemical reactor system. Results show improved control accuracy and robustness compared to conventional Lyapunov-based adaptive neural controllers. Overall, HPAS introduces a novel framework that enhances adaptability and performance in nonlinear system control.