Topology Identification of Complex Dynamical Networks with Stochastic Perturbations

Complex networks widely exist in our world, thus attracts extensive attentions from the multidisciplinary nonlinear science community. Many existing papers investigated the geometric features, control and synchronization of complex dynamical networks provided with presumably known structures. While in many practical situations, the exact topology of a network is usually unknown or uncertain. Therefore, topology identification is of great importance in the research of complex networks. Moreover, noise is ubiquitous in nature and in man-made systems. Based on the LaSalle Invariance Principle of stochastic differential equation, an adaptive estimation technique is proposed to identify the exact topology of a weighted general complex dynamical network with stochastic perturbations. The validity of the proposed approach is illustrated with a coupled Duffing network.