Robust Fractional-Order Adaptive Neural Network Control: A Rigorous Framework and Comparative Analysis

The control of uncertain, nonlinear systems remains a significant and persistent challenge in modern engineering. This paper introduces a comprehensive Fractional-Order Radial Basis Function Model Reference Adaptive Control (FO-RBF-MRAC) system, uniting the strengths of MRAC, RBF networks, and fractional calculus into a single, robust architecture. The theoretical contribution is two-fold: a novel, robust fractional-order adaptation law is proposed, and the Uniformly Ultimately Bounded (UUB) stability of the complete, integrated system is rigorously proven using a detailed fractional-order Lyapunov analysis. Crucially, the controller’s efficacy is validated through a comparative simulation study on an inverted pendulum. The proposed FO-RBF-MRAC is benchmarked against its integer-order equivalent and a state-of-the-art, well-tuned Model Predictive Controller (MPC). The results demonstrate that the proposed controller achieves performance comparable to the MPC under ideal nominal conditions, but exhibits vastly superior tracking accuracy and stability when faced with significant parametric uncertainties and external noise.