Synchronization for chaotic neural networks based on sampled data: a novel neuroscience technology using time-squared augmented Lyapunov functional

JOURNAL/atin/04.03/02274269-990000000-00013/figure1/v/2025-09-25T132225Z/r/image-tiff Chaotic neural networks, which incorporate chaotic dynamics into artificial neural architectures, demonstrate substantially richer dynamical behavior and enhanced nonlinear information processing capabilities than conventional networks. However, synchronization control subject to actuator saturation still faces challenges such as excessive conservativeness and insufficient utilization of sampled information. Targeting sampled-data synchronization control for chaotic neural networks, a novel neuroscience-based technique is proposed, leveraging the two-side-looped Lyapunov functionals and negative definiteness lemmas, aiming to enhancing the information processing capacity and synchronization accuracy of complex systems. This study investigated the problem of sampled-data synchronization control for chaotic neural networks under actuator saturation. First, a novel augmented Lyapunov functional, incorporating the square of the input delay, is constructed using the two-side-looped functional technique. Then, a wider range of coupling relationships among the aperiodic sampling information are comprehensively considered by introducing time-squared input-delay polynomials in the derivatives of the proposed functional. Leveraging a negative definiteness lemma, a less conservative stability criterion governing the chaotic neural network system is derived. Subsequently, a state feedback controller based on sampled data is designed to synchronize the drive system and the response system regionally, thereby further reducing the conservatism inherent in the synchronization results. Finally, numerical examples verify the effectiveness and superiority of the proposed method. Overall, this technique offers a novel approach for reliable chaotic neural network control, with potential extensions to multi-agent systems and brain science, advancing neuromorphic computing and brain-inspired intelligence. This achievement marks a significant neuroscience-control theory breakthrough, establishing a theoretical basis for intelligent control of complex nonlinear systems.