Abstract
The state observer for dynamic links in complex dynamical networks (CDNs) is investigated by using the adaptive method whether the networks are undirected or directed. In this paper, a complete network model is proposed, which is composed of two coupled subsystems called nodes subsystem and links subsystem, respectively. Especially, for the links subsystem, associated with some assumptions, the state observer with parameter adaptive law is designed. Compared to the existing results about the state observer design of CDNs, the advantage of this method is that a estimation problem of dynamic links is solved in directed networks for the first time. Finally, the results obtained in this paper are demonstrated by performing a numerical example.
Highlights
In recent past decades, the research on complex dynamical networks (CDNs) has become a hot topic in many fields [1,2,3,4]
Inspired by the above discussions, this paper mainly focuses on the state observer design for dynamic links in directed networks
A mathematical model for a class of directed CDNs is proposed, which is described by both the nodes subsystem and links subsystem with coupling between the two subsystems, and we have designed a state observer for the links subsystem by using the adaptive method. is means that a state estimation problem of dynamic links in directed networks is solved for the first time, which is regarded as the biggest contribution of this paper
Summary
The research on CDNs has become a hot topic in many fields [1,2,3,4]. From the above results about the synchronization, stabilization, consensus, or other problems of CDNs, it is easy to see all states in CDNs, including the states of nodes and links, are required to be measured accurately. A mathematical model for a class of directed CDNs is proposed, which is described by both the nodes subsystem and links subsystem with coupling between the two subsystems, and we have designed a state observer for the links subsystem by using the adaptive method. Notations. e n-dimensional Euclidean space is denoted as Rn, the set of n × n real matrices is denoted as Rn×n, the Euclidean norm of a vector or a matrix is denoted as ‖ · ‖, and the transpose of matrix A and n-dimensional identity matrix is denoted as AT and In, respectively
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