Topology identification for multi-layer complex dynamical networks with coupling time delay

This paper studies the topology identification for a multi-layer complex dynamical network model with the same number of nodes in each layer and arbitrary connections linking nodes from different layers. Since the coupling time delay is common, whose impact cannot be ignored. This paper proposes a new topology identification scheme for the multi-layer complex dynamical network. First, the original network is regarded as a drive network. In order to identify the topology of the drive network, a response network with the same node dynamics is constructed based on the design of the adaptive feedback controller. Then the error dynamical network is obtained. The Lyapunov stability theory is used to prove the asymptotic stability of the error dynamical network. When the response network is synchronized with the drive network, the topology of the original network could be identified by the response network. Finally, a numerical example is shown to demonstrate the effectiveness of the proposed topology identification scheme.