Memory-based adaptive event-triggered secure control of Markovian jumping neural networks suffering from deception attacks

In this article, we study the secure control of the Markovian jumping neural networks(MJNNs) subject to deception attacks.Considering the limitation of the network bandwidth and the impact of the deception attacks, we propose two memory-based adaptive event-trigger mechanisms(AETMs). Different from the available event-trigger mechanisms, these two memory-based AETMs contain the historical triggered data not only in the triggering conditions, but also in the adaptive law. They can adjust the data transmission rate adaptively so as to alleviate the impact of deception attacks on the controlled system and to suppress the peak of the system response. In view of the proposed memory-based AETMs, a time-dependent Lyapunov functional is constructed to analyze the stability of the error system. Some sufficient conditions to ensure the asymptotical synchronization of master-slave MJNNs are obtained, and two easy-to-implement co-design algorithms for the feedback gain matrix and the trigger matrix are given. Finally, a numerical example is given to verify the feasibility and superiority of the two memory-based AETMs.