Three Time Scales Modeling of the Undirected Clustered Network

Adhikari, Bikash; Panteley, Elena; Morărescu, Irinel-Constantin

doi:10.1109/cdc51059.2022.9992973

Cited by 3 publications

(3 citation statements)

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“…In [14], for undirected networks of linear systems, the authors explore modular networks with linear dynamics and emphasize the presence of three-time scales in the synchronization of interconnected agents in modular networks. Then, under some assumptions, the network dynamics can be approximated using a two-parameter singular-perturbation form.…”

Section: Introductionmentioning

confidence: 99%

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Analysis and Control of Multi-timescale Modular Directed Heterogeneous Networks

Lazri,

Panteley,

Loría

2024

IEEE Trans. Control Netw. Syst.

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We examine the collective behavior of largescale networks of heterogeneous nonlinear systems with directed weighted interconnections, and containing a spanning tree. We consider networks that are composed of groups of densely interconnected nodes, called modules, that are in turn sparsely interconnected. Such networks are called modular. The modules represent sub-networks wherein consensus may be rapidly achieved, while synchronization among modules occurs at a lower pace. Furthermore, relying on the framework of [1], we identify an underlying dynamics that corresponds to a weighted average of the nodes' respective states. This average dynamics evolves on a yet slower time-scale. Such triple time-scale make modular networks are amenable to be analyzed via singular-perturbations theory. We show that if the nodes' dynamics are semi-passive and the average dynamics is globally asymptotically stable, so is the entire network. In the case that the average dynamics is not globally asymptotically stable we show how our main analysis statement can be used for network control, via the addition of control nodes, in order to globally asymptotically stabilize the network.

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Section: Introductionmentioning

confidence: 99%

“…In this paper we analyze modular networks using a tripletime-scale model and give mild sufficient conditions for global asymptotic stability of the origin. Relative to [14] we consider directed networks of heterogeneous nonlinear semi-passive [15] systems. Relative to [11] we consider networks evolving in three time scales.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Control of Multi-timescale Modular Directed Heterogeneous Networks

Lazri,

Panteley,

Loría

2024

IEEE Trans. Control Netw. Syst.

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“…In addition to control problems, analysis problems have also been addressed for systems with three different time scales. In [14] the authors study the synchronization of linear systems interconnected over a modular network. In order to explain the three-time scales behavior, the authors use transformations taking into account the spectral properties of the network Laplacian.…”

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confidence: 99%

On Global Asymptotic Stability of Heterogeneous Modular Networks with Three Time-Scales

Lazri,

Panteley,

Loría

2023

2023 9th International Conference on Control, Decision and Information Technologies (CoDIT)

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We analyze the collective behavior of relatively large networks with the characteristic that nodes may be compartmentalized in modules. These are groups of systems that may be regarded as subnetworks in which each group of nodes achieves consensus with a certain rapidity. The dynamics of such networks exhibit, at least, two time-scales, for which singular perturbation methods may be used to assess the overall behavior. In this paper, we demonstrate that there are actually three natural time-scales and, accordingly, three interconnected dynamical systems with distinct speeds of convergence coexist. Our main statement establishes conditions for global asymptotic stability of the origin in such networked systems. In particular, we focus on bilinear heterogeneous systems and provide an illustrative example concerning chaotic oscillators. I. INTRODUCTIONModular networks are, generally speaking, networks of a large number of nodes that are compartmentalised in groups of nodes called modules. These are sparsely connected among themselves and the nodes contained within are densely interconnected [1], [2], [3]. Because of their complexity and large dimension, they are difficult to analyze; one approach consists in considering many agents in a module as a single node. This approach has been used both for undirected [4], [5], [6] and directed networks [7], [8]. This view is specially fit in networks such that agents within a module reach consensus relatively fast, before achieving consensus with nodes of other modules. Or, in other words, modules that have reached their own individual consensus find agreement among themselves at a slower pace [6], [9]. This is specially true if the coupling gain within a module is considerably larger than the one amongst modules.Such considerations lead naturally to multi-time scale models that can be studied using singular-perturbation theory [10], using the inverse of the coupling gain as singular parameter [11]. In the latter, is used to define a two-time scale modelling of a heterogeneous network ; the authors show that the emergent dynamics correspond to a slow subsystem while the synchronization errors form a fast subsystem. Singular perturbation is also used in [12] to show that, for interconnected linear systems with switching interconnection topology and linear coupling, if the coupling gain is sufficiently high, the synchronized behavior can be approximated by a reduced order switching system.

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