Robust Adaptive Neural Network Control for a Class of Uncertain Fractional-Order Chaotic Systems

Introduction: Fractional-order chaotic systems offer a more accurate representation of complex dynamical processes characterized by memory and hereditary properties. However, achieving stability in the presence of unstructured uncertainties and unknown nonlinearities remains a significant theoretical challenge in the field of non-integer calculus and control theory.

Methods: This paper proposes a robust adaptive neural network control strategy designed for a class of uncertain fractional-order chaotic systems. Utilizing the universal approximation capabilities of Radial Basis Function (RBF) neural networks, the proposed controller identifies and compensates for system uncertainties online through a deterministic adaptation law. Unlike traditional model-dependent approaches, this framework requires no a priori knowledge of system parameters. A rigorous stability analysis is conducted using the fractional-order Lyapunov direct method.

Results: The theoretical analysis proves that the closed-loop system is Mittag–Leffler stable and that the tracking errors converge to a compact neighborhood of the origin. Numerical simulations performed on benchmark chaotic attractors validate the effectiveness and robustness of the proposed neural-adaptive scheme, showing high precision in trajectory tracking even under significant external perturbations.

Conclusion: The proposed strategy provides a mathematically sound foundation for the control of complex fractional dynamics. By integrating RBF neural networks with fractional Lyapunov stability theory, this research offers a robust solution for synchronizing or controlling chaotic systems where mathematical models are partially or entirely unknown.