Predefined-Time Synchronization of Different Dimensional Neural Networks with Time-Varying Delays

In this paper, an adaptive predefined-time synchronization controller is designed for different dimensional neural networks with time-varying delays and unknown parameters. A new sufficient condition, which can be used to check whether the synchronization errors enter an arbitrarily small region within a user-defined time, is derived. Then, a controller combined with parameter adaptation laws, capable of guaranteeing predefined-time synchronization, is proposed for different dimensional neural networks. In particular, the convergence time and accuracy of the synchronization errors can be preset, which facilitates the control method design to meet the desired requirement. More notably, the proposed control approach corrects the singular problem in some previous works. A numerical result is given to verify the effectiveness of the developed method.