Improved Results on Fixed-/Preassigned-Time Synchronization for Memristive Complex-Valued Neural Networks.

Abstract

This article concerns the problems of synchronization in a fixed time or prespecified time for memristive complex-valued neural networks (MCVNNs), in which the state variables, activation functions, rates of neuron self-inhibition, neural connection memristive weights, and external inputs are all assumed to be complex-valued. First, the more comprehensive fixed-time stability theorem and more accurate estimations on settling time (ST) are systematically established by using the comparison principle. Second, by introducing different norms of complex numbers instead of decomposing the complex-valued system into real and imaginary parts, we successfully design several simpler discontinuous controllers to acquire much improved fixed-time synchronization (FXTS) results. Third, based on similar mathematical derivations, the preassigned-time synchronization (PATS) conditions are explored by newly developed new control strategies, in which ST can be prespecified and is independent of initial values and any parameters of neural networks and controllers. Finally, numerical simulations are provided to illustrate the effectiveness and superiority of the improved synchronization methodology.