Resilient-Sampling-Based Bipartite Synchronization of Cooperative-Antagonistic Neural Networks With Hybrid Attacks: Designing Interval-Dependent Functions

This paper investigates the bipartite synchronization problem of cooperative-antagonistic neural networks (CANNs) that suffer from hybrid attacks, i.e., denial-of-service (DoS) attacks and replay attacks. A resilient sampled-data control scheme is proposed to deal with the hybrid attacks. In addition, the Laplacian matrix with zero-row-sum is obtained based on the coordinate transformation method. On this basis, an easy-to-handle error system is constructed by integrating the sampling scheme, cooperative-antagonistic interactions and hybrid attacks. Subsequently, an interval-dependent function is designed by considering the characteristics of both replay and DoS attacks. Based on this, using Lyapunov function methods, inequality techniques, and other mathematical skills, some sufficient criteria are obtained for the bipartite synchronization of CANNs. Finally, three algorithms are proposed to minimize the coupling strength, or maximize the replay attack rate or the DoS attack rate, respectively. The effectiveness of the proposed control schemes and the advantages of the interval-dependent function are verified through numerical examples. Note to Practitioners —This work addresses the bipartite synchronization control problem of CANNs, which can be applied to some practical systems such as drone bidirectional formation and team competition. For example, the dynamics of drones within the same formation, including their velocity and position, are consistent with each other but opposite to those of other teams. Additionally, network systems across various industries often encounter DoS attacks or replay attacks during network transmission. A resilient sampled-data control scheme is proposed, and a Lyapunov function dependent on intervals is designed,taking into account the characteristics of the attack. Then, some algorithms are presented to minimize the allowable coupling strength or maximizing the allowable replay attack rate and DoS attack rate. Preliminary simulation experiments indicate that this sampling scheme is feasible. The types of network attacks are diverse. Therefore, obtaining system synchronization control schemes for more complex network attacks is a challenge.