Skip to main content

2016 | OriginalPaper | Buchkapitel

On the Optimal Control of Opinion Dynamics on Evolving Networks

verfasst von : Giacomo Albi, Lorenzo Pareschi, Mattia Zanella

Erschienen in: System Modeling and Optimization

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this work we are interested in the modelling and control of opinion dynamics spreading on a time evolving network with scale-free asymptotic degree distribution. The mathematical model is formulated as a coupling of an opinion alignment system with a probabilistic description of the network. The optimal control problem aims at forcing consensus over the network, to this goal a control strategy based on the degree of connection of each agent has been designed. A numerical method based on a model predictive strategy is then developed and different numerical tests are reported. The results show that in this way it is possible to drive the overall opinion toward a desired state even if we control only a suitable fraction of the nodes.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. phys. 74(1), 47–97 (2002) Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. phys. 74(1), 47–97 (2002)
2.
Zurück zum Zitat Albi, G., Bongini, M., Cristiani, E., Kalise, D.: Invisible control of self-organizing agents leaving unknown environments. SIAM J. Appl. Math 76, 1683–1710 (2016). in pressMathSciNetCrossRefMATH Albi, G., Bongini, M., Cristiani, E., Kalise, D.: Invisible control of self-organizing agents leaving unknown environments. SIAM J. Appl. Math 76, 1683–1710 (2016). in pressMathSciNetCrossRefMATH
3.
Zurück zum Zitat Albi, G., Herty, M., Pareschi, L.: Kinetic description of optimal control problems and applications to opinion consensus. Commun. Math. Sci. 13(6), 1407–1429 (2015)MathSciNetCrossRefMATH Albi, G., Herty, M., Pareschi, L.: Kinetic description of optimal control problems and applications to opinion consensus. Commun. Math. Sci. 13(6), 1407–1429 (2015)MathSciNetCrossRefMATH
4.
Zurück zum Zitat Albi, G., Pareschi, L., Zanella, M.: Boltzmann-type control of opinion consensus through leaders. Philos. Trans. R. Soc. A 372(2028), 20140138 (2014)MathSciNetCrossRefMATH Albi, G., Pareschi, L., Zanella, M.: Boltzmann-type control of opinion consensus through leaders. Philos. Trans. R. Soc. A 372(2028), 20140138 (2014)MathSciNetCrossRefMATH
5.
Zurück zum Zitat Albi, G., Pareschi, L., Zanella, M.: Uncertainty quantification in control problems for flocking models. Math. Prob. Eng. 2015, 850124 (2015). 14 pMathSciNetCrossRef Albi, G., Pareschi, L., Zanella, M.: Uncertainty quantification in control problems for flocking models. Math. Prob. Eng. 2015, 850124 (2015). 14 pMathSciNetCrossRef
6.
Zurück zum Zitat Albi, G., Pareschi, L., Zanella, M.: Opinion dynamics over complex networks: kinetic modeling and numerical methods. Kinet. Relat. Models 10(1), 1–32 (2017)MathSciNetCrossRefMATH Albi, G., Pareschi, L., Zanella, M.: Opinion dynamics over complex networks: kinetic modeling and numerical methods. Kinet. Relat. Models 10(1), 1–32 (2017)MathSciNetCrossRefMATH
7.
Zurück zum Zitat Amaral, L.A.N., Scala, A., Barthélemy, M., Stanley, H.E.: Classes of small-world networks. Proc. Natl. Acad. Sci. U. S. Am. 97(21), 11149–11152 (2000)CrossRef Amaral, L.A.N., Scala, A., Barthélemy, M., Stanley, H.E.: Classes of small-world networks. Proc. Natl. Acad. Sci. U. S. Am. 97(21), 11149–11152 (2000)CrossRef
8.
Zurück zum Zitat Barabási, A.-L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Phys. A: Stat. Meach. Appl. 272(1), 173–187 (1999)CrossRef Barabási, A.-L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Phys. A: Stat. Meach. Appl. 272(1), 173–187 (1999)CrossRef
9.
Zurück zum Zitat Barrat, A., Barthélemy, M., Vespignani, A.: Dynamical Processes on Complex Networks. Cambridge University Press, Cambridge (2008)CrossRefMATH Barrat, A., Barthélemy, M., Vespignani, A.: Dynamical Processes on Complex Networks. Cambridge University Press, Cambridge (2008)CrossRefMATH
10.
Zurück zum Zitat Benczik, I.J., Benczick, S.Z., Schmittmann, B., Zia, R.K.: Opinion dynamics on an adaptive random network. Phys. Rev. E 79(4), 046104 (2009)CrossRef Benczik, I.J., Benczick, S.Z., Schmittmann, B., Zia, R.K.: Opinion dynamics on an adaptive random network. Phys. Rev. E 79(4), 046104 (2009)CrossRef
11.
Zurück zum Zitat Bongini, M., Fornasier, M., Fröhlich, F., Haghverdi, L.: Sparse stabilization of dynamical systems driven by attraction and avoidance forces. Netw. Heterogen. Media 9(1), 1–31 (2014)MathSciNetCrossRefMATH Bongini, M., Fornasier, M., Fröhlich, F., Haghverdi, L.: Sparse stabilization of dynamical systems driven by attraction and avoidance forces. Netw. Heterogen. Media 9(1), 1–31 (2014)MathSciNetCrossRefMATH
12.
Zurück zum Zitat Wongkaew, S., Caponigro, M., Borzì, A.: On the control through leadership of the Hegselmann-Krause opinion formation model. Math. Models Methods Appl. Sci. 25(2), 255–282 (2015)MathSciNetCrossRefMATH Wongkaew, S., Caponigro, M., Borzì, A.: On the control through leadership of the Hegselmann-Krause opinion formation model. Math. Models Methods Appl. Sci. 25(2), 255–282 (2015)MathSciNetCrossRefMATH
13.
Zurück zum Zitat Chi, L.: Binary opinion dynamics with noise on random networks. Chin. Sci. Bull. 56(34), 3630–3632 (2011)CrossRef Chi, L.: Binary opinion dynamics with noise on random networks. Chin. Sci. Bull. 56(34), 3630–3632 (2011)CrossRef
14.
Zurück zum Zitat Das, A., Gollapudi, S., Munagala, K.: Modeling opinion dynamics in social networks. In: Proceedings of the 7th ACM International Conference on Web Search and Data Mining, ACM (2014) Das, A., Gollapudi, S., Munagala, K.: Modeling opinion dynamics in social networks. In: Proceedings of the 7th ACM International Conference on Web Search and Data Mining, ACM (2014)
15.
Zurück zum Zitat Herty, M., Zanella, M.: Performance bounds for the mean-field limit of constrained dynamics. Preprint (2015) Herty, M., Zanella, M.: Performance bounds for the mean-field limit of constrained dynamics. Preprint (2015)
16.
Zurück zum Zitat Jin, E.M., Girvan, M., Newman, M.E.J.: Structure of growing social networks. Phys. Rev. E 64(4), 046132 (2001)CrossRef Jin, E.M., Girvan, M., Newman, M.E.J.: Structure of growing social networks. Phys. Rev. E 64(4), 046132 (2001)CrossRef
17.
Zurück zum Zitat Kramer, A.D.I., Guillory, J.E., Hancock, J.T.: Experimental evidence of massive scale emotional contagion through social networks. Proc. Nat. Acad. Sci. 111(24), 8788–8789 (2014)CrossRef Kramer, A.D.I., Guillory, J.E., Hancock, J.T.: Experimental evidence of massive scale emotional contagion through social networks. Proc. Nat. Acad. Sci. 111(24), 8788–8789 (2014)CrossRef
19.
Zurück zum Zitat Pareschi, L., Toscani, G.: Interacting Multiagent Systems. Kinetic Equations and Monte Carlo Methods. Oxford University Press, Oxford (2013)MATH Pareschi, L., Toscani, G.: Interacting Multiagent Systems. Kinetic Equations and Monte Carlo Methods. Oxford University Press, Oxford (2013)MATH
20.
Zurück zum Zitat Strogatz, S.H.: Exploring complex networks. Nature 410(6825), 268–276 (2001)CrossRef Strogatz, S.H.: Exploring complex networks. Nature 410(6825), 268–276 (2001)CrossRef
21.
Zurück zum Zitat Sznajd-Weron, K., Sznajd, J.: Opinion evolution in closed community. Int. J. Mod. Phys. C 11(6), 1157–1165 (2000)CrossRefMATH Sznajd-Weron, K., Sznajd, J.: Opinion evolution in closed community. Int. J. Mod. Phys. C 11(6), 1157–1165 (2000)CrossRefMATH
22.
Zurück zum Zitat Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)CrossRef Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)CrossRef
23.
Zurück zum Zitat Weisbuch, G.: Bounded confidence and social networks. Eur. Phys. J. B-Condens. Matter Complex Syst. 38(2), 339–343 (2004)CrossRef Weisbuch, G.: Bounded confidence and social networks. Eur. Phys. J. B-Condens. Matter Complex Syst. 38(2), 339–343 (2004)CrossRef
24.
Zurück zum Zitat Xie, Y.-B., Zhou, T., Wang, B.-H.: Scale-free networks without growth. Phys. A 387, 1683–1688 (2008)CrossRef Xie, Y.-B., Zhou, T., Wang, B.-H.: Scale-free networks without growth. Phys. A 387, 1683–1688 (2008)CrossRef
Metadaten
Titel
On the Optimal Control of Opinion Dynamics on Evolving Networks
verfasst von
Giacomo Albi
Lorenzo Pareschi
Mattia Zanella
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-55795-3_4