Adaptive hybrid synchronisation in uncertain Kuramoto networks with limited information. Issue 9 (1st June 2019)

• Record Type: Journal Article
• Authors: Baldi, Simone; Tao, Tian; Kosmatopoulos, Elias B.
• Is Part Of: IET control theory & applications. Volume 13:Issue 9(2019)
• Page Start: 1229
• Page End: 1238
• Publication Date: 2019-06-01
• Subjects: quantisation (signal) -- distributed control -- Lyapunov methods -- protocols -- numerical analysis -- synchronisation -- adaptive control -- uncertain systems -- graph theory; communication network -- undirected connected graph -- appropriate adaptive protocols -- quantised information -- frequency synchronisation -- dynamic quantiser -- adaptive mechanism -- adaptive hybrid synchronisation strategy -- uncertain Kuramoto networks -- integrated adaptation -- quantisation protocol -- asymptotic synchronisation -- Kuramoto units -- zooming‐based quantisation approach -- distributed Lyapunov function; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2018.5465
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : 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.