Abstract
A great deal of attention from various scientific communities has been recently drawn to complex network systems (CNSs), with many profound results established in this active research field. This article provides a state-of-the-art survey on coordination and control of CNSs with switching network topologies, with emphasis on relationships between the switchings among different topology candidates and the network controllability, and between the switchings among different topology candidates and the emergence of coordination behaviors (including synchronization, consensus, and containment) of such CNSs. First, some fundamental properties of CNSs and the essentials of analytical methodologies for the stability of the fixed point of switched dynamical systems are briefly reviewed. Then, network controllability and the emergence of coordination behaviors of CNSs with switching topologies and the corresponding analytical approaches are discussed in detail, where some of the existing results along these topics are presented in a tutorial-like fashion. This article ends by presenting some interesting future research topics on the coordination and control of CNSs with switching topologies.
Highlights
F AR FROM being separate entities, many social and engineering systems can be considered as complex network systems (CNSs) associated with tight interactions among neighboring entities within them [1]–[4]
It is noted that research on the controllability of CNSs with inherent switching dynamics is still at its infancy stage, though quite a few results on the controllability of CNSs with switching topologies have been reported in the literature
We have surveyed some recent developments on coordination and control of CNSs with switching topologies
Summary
F AR FROM being separate entities, many social and engineering systems can be considered as complex network systems (CNSs) associated with tight interactions among neighboring entities within them [1]–[4]. Synchronizationregion-based analysis approaches [17], [35] are powerful tools for analyzing synchronization of coupling dynamical systems with fixed topology, such approaches are invalid to synchronization of CNSs with switching topologies as there generally does not exist a common similarity transformation to simultaneously convert the Laplacian matrices of all possible interaction graphs (communication topologies) to their corresponding Jordan canonical forms. A number of new methods have been developed in the literature during the last decade to analyze the network controllability and explore the emergence mechanisms for various coordination behaviors of CNSs with switching topologies, which are not covered in existing surveys [41]–[44] and tutorials [12], [32], [45].
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