Synchronization of complex networks in discrete-time for trajectory tracking using neural sliding modes with pinning control

This paper considers a novel solution for synchronization of complex networks in discrete-time, based on Lyapunov theory and passivity degree to define a reliable interval of coupling strength required to achieve synchronization in a directed complex network with non-identical nodes. By means of a discrete-time recurrent high-order neural network trained with an extended Kalman filter algorithm, the unknows pinned nodes are identified. Later, using an adaptive approach of sliding modes in discrete-time to complex networks, a selected pin node is locally controlled to guarantee trajectory tracking. Once the pin node is controlled, network synchronization is achieved, all its nodes follow selected trajectories. The results are illustrated via simulations considering that each node corresponds to a discretized nonlinear chaotic attractor.