Protocol-Based Synchronization of Semi-Markovian Jump Neural Networks With DoS Attacks and Application to Quadruple-Tank Process

This paper deals with the synchronization for semi-Markovian jump neural networks (S-MJNNs) with DoS attacks and adaptive event-triggered protocol. Aiming at reducing some conservatism of sojourn-time-exponential distribution of Markovian process, the semi-Markovian process is adopted to describe the sudden changes in structures and parameters. As a class of networked systems, the securities of dynamical systems are vulnerable to the DoS attacks that are supposed to obey the frequency constraint. First, on the basis of fully considering the characteristics of aperiodic DoS attacks, a feedback controller is constructed to realize the synchronization among the master-slave systems, in which an adaptive event-triggered protocol is adopted to adjust the amount of triggered data and save network resources more effectively than traditional event-triggered protocol. Then, sufficient conditions to ensure the exponential synchronization and solvable controller gain of the underlying S-MJNNs are given by means of stochastic Lyapunov stability and integral inequality. Finally, the quadruple-tank process model is shown to verify the proposed method. Note to Practitioners —As one of the research hotspots of neural networks, synchronization plays a crucial role in pattern recognition, associative memory, and information science. With the development of computer science and network technology, the information transmission is carried out through the network in the synchronized control of neural networks, which is bound to be affected by the non-ideal network environment. Therefore, the research on synchronization control should not only consider the realization of control method, but also consider the influence of network delay, cyber attacks, and other non-ideal network environment on system performance from the perspective of communication network. In this paper, the synchronization is studied for S-MJNNs with DoS attacks and adaptive event-triggered protocol. On the basis of fully considering the characteristics of aperiodic DoS attacks, the synchronization among the master-slave systems is realized by means of multiple Lyapunov functions and integral inequality. This study provides a new method for the practitioners to study the synchronization control strategy of neural networks affected by the cyber attacks.