Adaptive hybrid synchronisation in uncertain Kuramoto networks with limited information

In this study, the authors study adaptive synchronisation in networks with Kuramoto units whose parameters are unknown and where measurements are quantised over the communication network (therefore information is limited). They show that, for an undirected connected graph, synchronisation is enabled...

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Bibliographic Details
Published in:IET control theory & applications 2019-06, Vol.13 (9), p.1229-1238
Main Authors: Baldi, Simone, Tao, Tian, Kosmatopoulos, Elias B
Format: Article
Language:English
Subjects:
adaptive control
adaptive hybrid synchronisation strategy
adaptive mechanism
appropriate adaptive protocols
asymptotic synchronisation
communication network
distributed control
distributed Lyapunov function
dynamic quantiser
frequency synchronisation
graph theory
integrated adaptation
Kuramoto units
Lyapunov methods
numerical analysis
protocols
quantisation (signal)
quantisation protocol
quantised information
Special Issue: Recent Advances in Control and Verification for Hybrid Systems
synchronisation
uncertain Kuramoto networks
uncertain systems
undirected connected graph
zooming‐based quantisation approach
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Summary:In this study, the authors study adaptive synchronisation in networks with Kuramoto units whose parameters are unknown and where measurements are quantised over the communication network (therefore information is limited). They show that, for an undirected connected graph, synchronisation is enabled via appropriate adaptive protocols that counteract the effect of heterogeneity, uncertainty and quantised information. In particular, to address heterogeneity and uncertainty, appropriate adaptive laws are designed to drive the network to frequency synchronisation; to address quantised information, a dynamic quantiser is introduced and embedded into the adaptive mechanism via a zooming-based approach (therefore with hybrid dynamics). The resulting protocol ends up being an adaptive hybrid synchronisation strategy that can be distributed throughout the network: the quantiser is co-designed with the controller, as typical for zooming-based quantisation. The proposed integrated adaptation+quantisation protocol guarantees asymptotic synchronisation to a desired frequency, which is shown via an appropriately designed distributed Lyapunov function. Numerical simulations are also used to demonstrate the effectiveness of the proposed protocol.
ISSN:1751-8644
1751-8652
1751-8652
DOI:10.1049/iet-cta.2018.5465