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Three time scales modeling of the undirected clustered network

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Abstract

Dynamics evolving on different time scales appear naturally in networks of clusters. In this paper, we emphasize that the synchronization of interconnected agents partitioned in clusters involves three time-scales. Using a coordinate transformation, we reformulate the overall closed-loop clustered network dynamics in new coordinates describing the mean-field dynamics, the intra-cluster and the inter-cluster synchronization error dynamics. Then, under realistic assumptions, we show that the network dynamics can be represented in a two-parameter standard singular perturbation form in the new coordinate. The mean-field dynamics, which is the network’s long-term behavior, evolve on the slowest time-scale. The intra-cluster error dynamics, which characterizes the synchronization inside clusters, evolve on the fastest time scale. Finally, the inter-cluster error dynamics, which characterizes the synchronization between clusters, is fast with respect to the mean-field one and slow with respect to the intra-cluster one. Using the two-parameter singular perturbation form, we establish approximations of the variables using standards techniques based on Tychonoff’s theorem. Numerical simulations validate our theoretical results.
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Dates and versions

hal-03754270 , version 1 (19-08-2022)

Identifiers

  • HAL Id : hal-03754270 , version 1

Cite

Bikash Adhikari, Elena Panteley, Irinel-Constantin Morarescu. Three time scales modeling of the undirected clustered network. 61st IEEE Conference on Decision and Control, CDC 2022, Dec 2022, Cancun, Mexico. ⟨hal-03754270⟩
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