Neural Lyapunov Control for Caputo Fractional-Order Systems

This article presents a novel neural network–based approach for designing effective control policies for Caputo-type nonlinear fractional-order systems. The proposed approach iteratively refines the neural network to generate a control policy that stabilizes the system within a predefined neighborhood around the zero equilibrium. Stability of the controlled system is guaranteed by rigorously formulated theorems and empirically verified using a neural Lyapunov function. The effectiveness of the proposed methodology is demonstrated through simulations on two classical Caputo fractional-order systems, showcasing its capability to ensure stability and its potential applicability to a broader range of fractional-order nonlinear systems.