Finite-time bumpless transfer synchronisation of discrete-time delayed positive neural networks under dual-channel false data inject attacks

This paper studies the finite-time synchronisation problem of discrete-time delayed positive neural networks under false data injection attacks. A master–slave networked control framework is constructed which is under dual-channel attacks, that is, the channel from sensor to controller and the channel from controller to actuator. False data injection attacks can destroy easily the positivity of positive neural networks, by injecting large negative data into the sampled signals, for instance. In this case, assuming a non-negative synchronisation error, as in previous work, to maintain the positivity of the slave system is inadequate. A newly designed regulator-based switching control method is proposed to synchronise the master–slave system decreasing the influence of dual-channel attacks. The positivity constraint in synchronisation error system is removed. To further reduce the turbulence caused by the switching of variable control inputs, a bumpless transfer strategy is considered. By using the Lyapunov theorem, some sufficient delay-dependent conditions for finite-time synchronisation of master–slave positive neural networks are proposed in the form of linear matrix inequalities. A numerical example and a water management system are presented to verify the effectiveness of the proposed methods.