Adaptive Event-Triggered Synchronization of Reaction–Diffusion Neural Networks

This article focuses on the design of an adaptive event-triggered sampled-data control (ETSDC) mechanism for synchronization of reaction-diffusion neural networks (RDNNs) with random time-varying delays. Different from the existing ETSDC schemes with predetermined constant thresholds, an adaptive ETSDC mechanism is proposed for RDNNs. The adaptive ETSDC mechanism can be promptly adaptively adjusted since the threshold function is based on the current sampled and latest transmitted signals. Thus, the adaptive ETSDC mechanism can effectively save communication resources for RDNNs. By taking the influence of uncertain factors, the random time-varying delays are considered, which belongs to two intervals in a probabilistic way. Then, by constructing an appropriate Lyapunov-Krasovskii functional (LKF), new synchronization criteria are derived for RDNNs. By solving a set of linear matrix inequalities (LMIs), the desired adaptive ETSDC gain is obtained. Finally, the merits of the adaptive ETSDC mechanism and the effectiveness of the proposed results are verified by one numerical example.