Consensus of double integrator multiagent systems under nonuniform sampling and changing topology

Ufuk Sevim; Leyla Goren-Sumer; Ufuk Sevim; Leyla Goren-Sumer

doi:10.3934/math.2023827

AIMS Mathematics

2023, Volume 8, Issue 7: 16175-16190. doi: 10.3934/math.2023827

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Research article

Consensus of double integrator multiagent systems under nonuniform sampling and changing topology

Ufuk Sevim ^,,
Leyla Goren-Sumer

Department of Control and Automation Engineering, Istanbul Technical University, Ayazaga, Istanbul, Turkey

Received: 09 March 2023 Revised: 20 April 2023 Accepted: 24 April 2023 Published: 06 May 2023
MSC : 93D50, 93C57

This article considers a consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. In the considered problem, the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in an arbitrarily selected region. Existence of a controller that ensures consensus in this setting is shown when the changing topology graphs are undirected and have a spanning tree. Also, explicit bounds for controller parameters are given. A sufficient condition is given to solve the consensus problem based on making the closed loop system matrix a contraction using a particular coordinate system for general linear dynamics. It is shown that the given condition immediately generalizes to changing topology in the case of undirected topology graphs. This condition is applied to double integrator dynamics to obtain explicit bounds on the controller.
- multiagent systems,
- consensus,
- nonuniform sampling,
- changing topology
Citation: Ufuk Sevim, Leyla Goren-Sumer. Consensus of double integrator multiagent systems under nonuniform sampling and changing topology[J]. AIMS Mathematics, 2023, 8(7): 16175-16190. doi: 10.3934/math.2023827

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Abstract

This article considers a consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. In the considered problem, the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in an arbitrarily selected region. Existence of a controller that ensures consensus in this setting is shown when the changing topology graphs are undirected and have a spanning tree. Also, explicit bounds for controller parameters are given. A sufficient condition is given to solve the consensus problem based on making the closed loop system matrix a contraction using a particular coordinate system for general linear dynamics. It is shown that the given condition immediately generalizes to changing topology in the case of undirected topology graphs. This condition is applied to double integrator dynamics to obtain explicit bounds on the controller.

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