In this paper we analyse the equilibrium configurations for the time-inverted Kuramoto Model with homogeneous agents and a fixed ring topology, where time-inverted means that the coupling between the different states is via a negative factor. This model exhibits a dual behaviour with respect to the classic Kuramoto Model with a positive coupling. In the paper, we show the existence of two possible stable equilibrium configurations: the splay state formation (1-clustered coverage) and the deployment in clusters (κ-clustered coverage). We provide sufficient conditions for the splay state formation and a stability analysis for the networked system. Moreover, we provide some initial results towards the controllability of the final equilibrium configurations. In particular, we lay the foundations to understand the conditions to switch between stable equilibria.

Time-Inverted Kuramoto Dynamics for κ-Clustered Circle Coverage / Boldrer, M.; Riz, F.; Pasqualetti, F.; Palopoli, L.; Fontanelli, D.. - ELETTRONICO. - (2021), pp. 1205-1211. ((Intervento presentato al convegno 60th IEEE Conference on Decision and Control, CDC 2021 tenutosi a usa nel December 2021 [10.1109/CDC45484.2021.9683310].

Time-Inverted Kuramoto Dynamics for κ-Clustered Circle Coverage

Boldrer M.;Riz F.;Palopoli L.;Fontanelli D.
2021

Abstract

In this paper we analyse the equilibrium configurations for the time-inverted Kuramoto Model with homogeneous agents and a fixed ring topology, where time-inverted means that the coupling between the different states is via a negative factor. This model exhibits a dual behaviour with respect to the classic Kuramoto Model with a positive coupling. In the paper, we show the existence of two possible stable equilibrium configurations: the splay state formation (1-clustered coverage) and the deployment in clusters (κ-clustered coverage). We provide sufficient conditions for the splay state formation and a stability analysis for the networked system. Moreover, we provide some initial results towards the controllability of the final equilibrium configurations. In particular, we lay the foundations to understand the conditions to switch between stable equilibria.
Proceedings of the IEEE Conference on Decision and Control
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Boldrer, M.; Riz, F.; Pasqualetti, F.; Palopoli, L.; Fontanelli, D.
Time-Inverted Kuramoto Dynamics for κ-Clustered Circle Coverage / Boldrer, M.; Riz, F.; Pasqualetti, F.; Palopoli, L.; Fontanelli, D.. - ELETTRONICO. - (2021), pp. 1205-1211. ((Intervento presentato al convegno 60th IEEE Conference on Decision and Control, CDC 2021 tenutosi a usa nel December 2021 [10.1109/CDC45484.2021.9683310].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/341375
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