Synchronization of multiple neural networks with reaction–diffusion terms under cyber–physical attacks

Abstract

In this paper, we investigate the synchronization problem of multiple neural networks with reaction–diffusion terms under cyber–physical attacks via distributed control. As for the multiagent systems, designing security control laws for multiple neural networks (MNNs) with reaction–diffusion terms is a big challenge when the proposed neural networks perform various cooperative tasks under failures or attacks. In complex environment, the MNNs with reaction–diffusion terms may be under mixed attacks, and one of them has been named cyber–physical attacks which would affect the communication links and nodes leading to the change of topology and states, as well as the distributed controllers. To deal with these issues, we will construct a novel Lyapunov function and combine with some properties of M-matrix to investigate the effects caused by cyber–physical attacks, and a security control law is also given to ensure the synchronization of the proposed neural network system. On the algorithmic side, it is worth mentioning that the security architecture and the security control algorithm are given to choose parameters of the feedback gain matrix and the coupling strength to achieve synchronization. Finally, a numerical simulation is given to support the obtained theoretical results.