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September  2015, 35(9): 4071-4094. doi: 10.3934/dcds.2015.35.4071

(Un)conditional consensus emergence under perturbed and decentralized feedback controls

1. 

Technische Universität München, Fakultät Mathematik, Boltzmannstraße 3, D-85748 Garching, Germany

2. 

Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraße 69, 4040 Linz

Received  April 2014 Revised  September 2014 Published  April 2015

We study the problem of consensus emergence in multi-agent systems via external feedback controllers. We consider a set of agents interacting with dynamics given by a Cucker-Smale type of model, and study its consensus stabilization by means of centralized and decentralized control configurations. We present a characterization of consensus emergence for systems with different feedback structures, such as leader-based configurations, perturbed information feedback, and feedback computed upon spatially confined information. We characterize consensus emergence for this latter design as a parameter-dependent transition regime between self-regulation and centralized feedback stabilization. Numerical experiments illustrate the different features of the proposed designs.
Citation: Mattia Bongini, Massimo Fornasier, Dante Kalise. (Un)conditional consensus emergence under perturbed and decentralized feedback controls. Discrete & Continuous Dynamical Systems, 2015, 35 (9) : 4071-4094. doi: 10.3934/dcds.2015.35.4071
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show all references

References:
[1]

Annu. Rev. Control, 32 (2008), 87-98. doi: 10.1016/j.arcontrol.2008.03.004.  Google Scholar

[2]

Proc. Natl. Acad. Sci. U.S.A., 105 (2008), 1232-1237. doi: 10.1073/pnas.0711437105.  Google Scholar

[3]

Math. Mod. Meth. Appl. Sci. (M3AS), 25 (2015), 521-564. doi: 10.1142/S0218202515400059.  Google Scholar

[4]

in Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences (eds. G. Naldi, L. Pareschi, G. Toscani and N. Bellomo), Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, (2010), 297-336. doi: 10.1007/978-0-8176-4946-3_12.  Google Scholar

[5]

MathS In Action, 1 (2008), 1-25. doi: 10.5802/msia.1.  Google Scholar

[6]

IEEE Trans. Automat. Control, 52 (2007), 852-862. doi: 10.1109/TAC.2007.895842.  Google Scholar

[7]

Jpn. J. Math., 2 (2007), 197-227. doi: 10.1007/s11537-007-0647-x.  Google Scholar

[8]

Volume 18 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1988. doi: 10.1007/978-94-015-7793-9.  Google Scholar

[9]

ESAIM, Control Optim. Calc. Var., 20 (2014), 1123-1152. doi: 10.1051/cocv/2014009.  Google Scholar

[10]

J. Phys. A: Math. Theor.l, 43 (2010), 315201, 19 pp. doi: 10.1088/1751-8113/43/31/315201.  Google Scholar

[11]

IEEE Trans. Automat. Control, 55 (2010), 1679-1683. doi: 10.1109/TAC.2010.2046113.  Google Scholar

[12]

J. Artif. Soc. Soc. Simulat., 5 (2002), 1-24. Google Scholar

[13]

Springer, 2013. doi: 10.1007/978-1-4471-4147-1.  Google Scholar

[14]

J. Dyn. Syst. Meas. Control , 129 (2007), 571-583. doi: 10.1115/1.2766721.  Google Scholar

[15]

IEEE Trans. Autom. Control, 49 (2004), 1520-1533. doi: 10.1109/TAC.2004.834113.  Google Scholar

[16]

Automatica, 50 (2014), 64-74. doi: 10.1016/j.automatica.2013.09.034.  Google Scholar

[17]

SIGGRAPH Comput. Graph., 21 (1987), 25-34. doi: 10.1145/37401.37406.  Google Scholar

[18]

Phys. Rev. Lett., 75 (1995), 1226-1229. doi: 10.1103/PhysRevLett.75.1226.  Google Scholar

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