Topology Identification of Multilink Complex Dynamical Networks via Adaptive Observers Incorporating Chaotic Exosignals

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.

Sparse Bayesian Learning for Switching Network Identification

Learning dynamical networks based on time series of nodal states is of significant interest in systems science, computer science, and control engineering. Despite recent progress in network identification, most research focuses on static structures rather than switching ones. Therefore, this article develops a method for identifying the structures of switching networks by exploring and leveraging both temporal and spatial structural information that characterizes the switching process. The proposed method employs a new sparse Bayesian learning algorithm based on coupled hyperblocks to estimate unknown switching instants. Experimental results on benchmark artificial and real networks are elaborated to demonstrate the effectiveness and superiority of the proposed method.

Identifying the switching topology of dynamical networks based on adaptive synchronization

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.

Identifying partial topology of simplicial complexes

This paper investigates partial topology identification of simplicial complexes based on adaptive synchronization. For the nodes of interest, the interactions that they participate in can be accurately reconstructed by designing adaptive controllers and parameter estimators. Particularly, not only pairwise interactions but a higher-order structure can be effectively recovered by our method. Moreover, a new linear independence condition with a rigorous definition is established for parameter estimators to converge asymptotically to the true values. Numerical simulations on a general two-dimensional simplicial complex as well as a real-world structure are provided to show the validity of the result and discuss the influence of different parameters on the identification process.

Topology Identification of Time-Scales Complex Networks

This paper studies a topology identification problem of complex networks with dynamics on different time scales. Using the adaptive synchronization method, some criteria for a successful estimation are obtained. In particular, by regulating the original network to synchronize with an auxiliary chaotic network, this work further explores a way to avoid the precondition of linear independence. When the adaptive controller fails to achieve the outer synchronization, an impulsive control method is used. In the end, we conclude with three numerical simulations. The results obtained in this paper generalize continuous, discrete with arbitrary time step size and mixed cases.