Identifying the switching topology of dynamical networks based on adaptive synchronization

Abstract

This paper proposes an approach for identifying unknown switching topology in a complex dynamical network. The setup is divided into two components: a primary drive network and a specialized response network equipped with switched topology observers. Each class of observers is dedicated to tracking a specific topology structure. The updating law for these observers is dynamically adjusted based on the operational status of the corresponding topology in the drive network—active if engaged and dormant if not. The sufficient conditions for successful identification are obtained by employing adaptive synchronization control and the Lyapunov function method. In particular, this paper abandons the generally used assumption of linear independence and adopts an easily verifiable condition for accurate identification. The result shows that the proposed identification method is applicable for any finite switching periods. By employing the chaotic Lü system and the Lorenz system as the local dynamics of the networks, numerical examples demonstrate the effectiveness of the proposed topology identification method.