Resilient Sampled-Data Control for Bipartite Synchronization of Cooperation-Competition Neural Networks Against Denial-of-Service Attacks

This paper deals with the bipartite synchronization problem of cooperation-competition neural networks (CCNNs) subject to denial-of-service (DoS) attacks. A resilient sampled-data control strategy is proposed to mitigate the adverse impact of DoS attacks, which takes both the attack signal and the periodic sampling communication protocol into account. The directed signed graph is introduced to characterize the cooperation and competition interactions among nodes. By leveraging coordinate transformation and graph theory techniques, a zero-row-sum Laplacian matrix is constructed to facilitate subsequent analysis. In combination with DoS attacks and control strategies, a tractable error system model is formulated. An interval-dependent function is further introduced, taking into account both attack intervals and data transmission intervals. Based on Lyapunov stability theory, the convex combination approach, and inequality techniques, the bipartite synchronization criteria for CCNNs are obtained. Moreover, the constructed interval-dependent function can improve the maximum allowable attack rate or reduce the minimum allowable coupling strength. The proposed control scheme is demonstrated to be effective and superior through the two numerical examples. Note to Practitioners—In many practical engineering and natural systems, cooperative and competitive behaviors often coexist and evolve dynamically. Directed signed graphs serve as an effective modeling tool for such interactions, in which positive and negative edge weights represent cooperation and competition, respectively. Bipartite synchronization provides a powerful framework for capturing these dynamics, offering a more accurate representation of real-world system behavior. However, networked control systems are increasingly vulnerable to DoS attacks, posing significant challenges to both robustness and control efficiency. To address these issues, this study proposes a resilient sampled-data control scheme that accounts for both periodic sampling protocols and DoS attacks. An interval-dependent function is constructed based on both the attack duration and data transmission intervals, thereby enhancing the tolerance to attacks or reducing the coupling strength. The effectiveness and superiority are validated through numerical examples, providing valuable insights into the secure coordination of multi-agent systems and the design of resilient industrial automation networks.