Synchronisation of heterogeneous Kuramoto oscillators with sampled information and a constant leader |
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Authors: | Jairo Giraldo Nicanor Quijano |
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Affiliation: | 1. Computer Science Department, University of Texas at Dallas
, Texas, United States;2. Departamento de Ingeniería Eléctrica y Electrónica, Universidad de los Andes
, Bogotá, Colombia |
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Abstract: | The Kuramoto oscillator has been widely studied because it can model a wide variety of engineering problems. Conditions for frequency synchronisation of a network of undirected coupled Kuramoto oscillators have been well established. However, the topology that describes the interaction between oscillators may not be connected due to environmental limitations or link failures. In this work we propose a consensus-based control strategy that forces the network to follow a virtual agent with a constant frequency, and where only few agents have access to the leader state. The controller is based on the exchange of information between the oscillators through a communication network. We introduce conditions for synchronisation and phase cohesiveness with the proposed control strategy that depends on the interaction between the physical topology and the communication topology. Finally, we study two applications to illustrate concepts presented in this work: (1) frequency synchronisation in smart grids; and (2) vehicle coordination. |
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Keywords: | Synchronisation Kuramoto oscillator networked control systems smart grids multi-agent systems sampled data |
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