An Improved Topology Identification Method of Complex Dynamical Networks

Over the past decade, numerous synchronization-based identification methods have been proposed to address the challenge of identifying unknown network topologies. The linear independence condition (LIC) is an essential requirement in these methods, however, there are issues with this condition. In this article, we propose an improved LIC-free synchronization-based identification method to address above issues. Specifically, a drive network consisting of isolated nodes that satisfy specific conditions is constructed, and the network containing an unknown topology is defined as the response network. Through the design of appropriate controllers and update laws, the drive network and the response network achieve synchronization, while the estimation matrix accurately identifies the unknown topology matrix. Our method is proven to be a generalized form of the existing LIC-free identification methods. Furthermore, we introduce a novel proof framework to theoretically demonstrate the effectiveness of our method. Finally, two simulation examples demonstrate the effectiveness of the proposed method.