Event-Triggered Quantized Synchronization via Sampled-Data Iterative Learning Control for Coupled Fractional-Order Time-Delayed Competitive Neural Networks

This paper examines the problem of achieving synchronization within fractional-order competitive neural networks (FOCNNs) affected by intrinsic transmission delays. To overcome the limitations associated with restricted network bandwidth and excessive computational expenses, a quantized sampled-data distributed iterative learning control (QSDILC) strategy is introduced. In contrast to conventional continuous-time methods, a precise quantizer and a variable sampling structure are explicitly integrated into the presented QSDILC law. Within this framework, the control trajectory of each individual node is adjusted relying entirely upon discretized, locally acquired error signals. Furthermore, an event-triggering scheme founded on the error energy attenuation (EEA) principle is formulated to maximize communication efficiency. Control signal refreshes are adaptively managed by this EEA-driven approach through the continuous tracking of how rapidly the synchronization error energy decays. Consequently, unnecessary iterative steps are eliminated while the strict convergence of the FOCNN states along the iteration axis is guaranteed. Through theoretical evaluation—relying on the fundamentals of fractional calculus and contraction mapping theory—the necessary criteria guaranteeing synchronization under the proposed QSDILC architecture are rigorously established. Numerical simulations demonstrate that communication overhead and computational burdens are significantly minimized by the integrated QSDILC and EEA-based event-triggered approach, all while a superior convergence speed is maintained, thereby offering a reference for addressing the synchronization control of time-delayed FOCNNs under limited communication and computational resources.