Parameter estimation and topology identification of uncertain fractional order complex networks

This paper focuses on a significant issue in the research of fractional order complex network, i.e., the identification problem of unknown system parameters and network topologies in uncertain complex networks with fractional-order node dynamics. Based on the stability analysis of fractional order systems and the adaptive control method, we propose a novel and general approach to address this challenge. The theoretical results in this paper have generalized the synchronization-based identification method that has been reported in several literatures on identifying integer order complex networks. We further derive the sufficient condition that ensures successful network identification. An uncertain complex network with four fractional-order Lorenz systems is employed to verify the effectiveness of the proposed approach. The numerical results show that this approach is applicable for online monitoring of the static or changing network topology. In addition, we present a discussion to explore which factor would influence the identification process. Certain interesting conclusions from the discussion are obtained, which reveal that large coupling strengths and small fractional orders are both harmful for a successful identification.