Resilient Synchronization of Neural Networks Under DoS Attacks and Communication Delays via Event-Triggered Impulsive Control

This article focuses on solving the synchronization problem of neural networks (NNs) in the presence of denial-of-service (DoS) attacks and communication delays. Specifically, an attack detection algorithm constructed based upon the acknowledgment (ACK) signal is provided to detect the sleeping and active intervals of DoS attacks. To reduce information transmission during the synchronization-seeking process, a new kind of Lyapunov function-based resilient event-triggered mechanism (ETM) is designed to modulate the information transmission between the master and slave systems. Then, an event-based impulsive controller is designed to achieve synchronization in the master-slave systems with event-triggered communication and communication delay between the event generator and the controller, where the impulsive control instants are produced by the resilient ETM rather than prescribed. Furthermore, a resilient sampled-data-based ETM and an event-based controller consisting of hybrid state feedback and impulsive controllers are developed. Under the proposed ETMs and controllers, some sufficient yet efficient criteria are derived to guarantee the master-slave synchronization of NNs. The influence of the attack parameters and triggering parameters on the synchronization performance is also discussed. Finally, two numerical examples and an application in image encryption and decryption based on the master-slave chaotic systems are given to demonstrate the effectiveness of the theoretical results.