Predefined-time synchronization of coupled neural networks with switching parameters and disturbed by Brownian motion.

This article focuses on predefined time synchronization problem for a class of signal switching neural networks with time-varying delays. In the network models, we not only consider the coupling characteristics in the following networks, but also consider the disturbance with standard Brownian motion. In the design of the controller, the control gain is designed as 1ɛ+T-t (t∈[T,T), ɛ is an optional smaller positive number), which avoids the infinite gain (the control gain is designed as 1T-t in other reference). In order to get the predefined time control law, a power function is multiplied to the Lyapunov functional, from which it can get an exponential upper bound function via the derivative and mathematical expectation operation. Utilizing the martingale theory and the method of Laplace matrix, some novel predefined time synchronization criteria are obtained for the leader-following neural networks, meanwhile the following networks can maintain the leader network after achieved synchronization. Based on the special network of the main system, five corollaries separately develop the predefined time synchronization results from different perspectives. An example with some simulation figures and computing results fully exhibits the effectiveness of the achieved synchronization scheme. In this case, although the error signal is disturbed by Brownian motion, the trace signal can still stably converge to zero by this control scheme, meanwhile the predefined-time control effect is achieved.