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2017 | OriginalPaper | Buchkapitel

Interaction Network, State Space, and Control in Social Dynamics

verfasst von : Aylin Aydoğdu, Marco Caponigro, Sean McQuade, Benedetto Piccoli, Nastassia Pouradier Duteil, Francesco Rossi, Emmanuel Trélat

Erschienen in: Active Particles, Volume 1

Verlag: Springer International Publishing

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Abstract

In the present chapter, we study the emergence of global patterns in large groups in first- and second-order multiagent systems, focusing on two ingredients that influence the dynamics: the interaction network and the state space. The state space determines the types of equilibrium that can be reached by the system. Meanwhile, convergence to specific equilibria depends on the connectivity of the interaction network and on the interaction potential. When the system does not satisfy the necessary conditions for convergence to the desired equilibrium, control can be exerted, both on finite-dimensional systems and on their mean-field limit.

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Literatur
1.
Zurück zum Zitat G. Albi, M. Bongini, E. Cristiani, and D. Kalise. Invisible control of self-organizing agents leaving unknown environments. SIAM Journal on Applied Mathematics. to appear. G. Albi, M. Bongini, E. Cristiani, and D. Kalise. Invisible control of self-organizing agents leaving unknown environments. SIAM Journal on Applied Mathematics. to appear.
2.
Zurück zum Zitat G. Albi, M. Herty, and L. Pareschi. Kinetic description of optimal control problems and applications to opinion consensus. Communications in Mathematical Sciences, 13(6):1407–1429, 2015.MathSciNetCrossRefMATH G. Albi, M. Herty, and L. Pareschi. Kinetic description of optimal control problems and applications to opinion consensus. Communications in Mathematical Sciences, 13(6):1407–1429, 2015.MathSciNetCrossRefMATH
3.
Zurück zum Zitat G. Albi and L. Pareschi. Selective model-predictive control for flocking systems. preprint. G. Albi and L. Pareschi. Selective model-predictive control for flocking systems. preprint.
4.
Zurück zum Zitat G. Albi and L. Pareschi. Modeling of self-organized systems interacting with a few indi- viduals: from microscopic to macroscopic dynamics. Applied Mathematics Letters, 26:397–401, 2013.MathSciNetCrossRefMATH G. Albi and L. Pareschi. Modeling of self-organized systems interacting with a few indi- viduals: from microscopic to macroscopic dynamics. Applied Mathematics Letters, 26:397–401, 2013.MathSciNetCrossRefMATH
5.
Zurück zum Zitat G. Albi, L. Pareschi, and M. Zanella. Boltzmann-type control of opinion consensus through leaders. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 372(2028), 2014.MATH G. Albi, L. Pareschi, and M. Zanella. Boltzmann-type control of opinion consensus through leaders. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 372(2028), 2014.MATH
6.
Zurück zum Zitat M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, and V. Zdravkovic. Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proceedings of the National Academy of Sciences, 105(4):1232–1237, 2008.CrossRef M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, and V. Zdravkovic. Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proceedings of the National Academy of Sciences, 105(4):1232–1237, 2008.CrossRef
7.
Zurück zum Zitat M. Bardi and F. S. Priuli. LQG mean-field games with ergodic cost. In 52nd IEEE Conference on Decision and Control, pages 2493–2498, Dec 2013. M. Bardi and F. S. Priuli. LQG mean-field games with ergodic cost. In 52nd IEEE Conference on Decision and Control, pages 2493–2498, Dec 2013.
8.
Zurück zum Zitat M. Bardi and F. S. Priuli. Linear-quadratic \(n\)-person and mean-field games with ergodic cost. SIAM Journal on Control and Optimization, 52(5):3022–3052, 2014.MathSciNetCrossRefMATH M. Bardi and F. S. Priuli. Linear-quadratic \(n\)-person and mean-field games with ergodic cost. SIAM Journal on Control and Optimization, 52(5):3022–3052, 2014.MathSciNetCrossRefMATH
9.
Zurück zum Zitat L. Behera and F. Schweitzer. On spatial consensus formation: Is the Sznajd model different from a voter model? International Journal of Modern Physics C, 14(10):1331–1354, 2003.CrossRef L. Behera and F. Schweitzer. On spatial consensus formation: Is the Sznajd model different from a voter model? International Journal of Modern Physics C, 14(10):1331–1354, 2003.CrossRef
10.
Zurück zum Zitat V. D. Blondel, J. M. Hendrickx, and J. N. Tsitsiklis. Continuous-time average-preserving opinion dynamics with opinion-dependent communications. SIAM Journal on Control and Optimization, 48(8):5214–5240, 2010.MathSciNetCrossRefMATH V. D. Blondel, J. M. Hendrickx, and J. N. Tsitsiklis. Continuous-time average-preserving opinion dynamics with opinion-dependent communications. SIAM Journal on Control and Optimization, 48(8):5214–5240, 2010.MathSciNetCrossRefMATH
11.
Zurück zum Zitat F. Bullo, J. Cortés, and S. Martínez. Distributed control of robotic networks: a mathematical approach to motion coordination algorithms. Princeton series in applied mathematics. Princeton University Press, Princeton, 2009.CrossRefMATH F. Bullo, J. Cortés, and S. Martínez. Distributed control of robotic networks: a mathematical approach to motion coordination algorithms. Princeton series in applied mathematics. Princeton University Press, Princeton, 2009.CrossRefMATH
12.
Zurück zum Zitat J. A. Cañizo, J. A. Carillo, and J. Rosado. A well-posedness theory in measures for some kinetic models of collective motion. Mathematical Models and Methods in Applied Sciences, 21(03):515–539, 2011.MathSciNetCrossRefMATH J. A. Cañizo, J. A. Carillo, and J. Rosado. A well-posedness theory in measures for some kinetic models of collective motion. Mathematical Models and Methods in Applied Sciences, 21(03):515–539, 2011.MathSciNetCrossRefMATH
13.
Zurück zum Zitat P. E. Caines. Encyclopedia of Systems and Control, chapter Mean Field Games, pages 1–6. Springer London, London, 2013. P. E. Caines. Encyclopedia of Systems and Control, chapter Mean Field Games, pages 1–6. Springer London, London, 2013.
14.
Zurück zum Zitat M. Caponigro, M. Fornasier, B. Piccoli, and E. Trélat. Sparse stabilization and optimal control of the Cucker–Smale model. Mathematical Control and Related Fields, 3:447–466, 2013.MathSciNetCrossRefMATH M. Caponigro, M. Fornasier, B. Piccoli, and E. Trélat. Sparse stabilization and optimal control of the Cucker–Smale model. Mathematical Control and Related Fields, 3:447–466, 2013.MathSciNetCrossRefMATH
15.
Zurück zum Zitat M. Caponigro, M. Fornasier, B. Piccoli, and E. Trélat. Sparse stabilization and control of alignment models. Mathematical Models and Methods in Applied Sciences, 25(3):521–564, 2015.MathSciNetCrossRefMATH M. Caponigro, M. Fornasier, B. Piccoli, and E. Trélat. Sparse stabilization and control of alignment models. Mathematical Models and Methods in Applied Sciences, 25(3):521–564, 2015.MathSciNetCrossRefMATH
16.
Zurück zum Zitat M. Caponigro, A. C. Lai, and B. Piccoli. A nonlinear model of opinion formation on the sphere. Discrete and Continuous Dynamical Systems Ser. A, (9):4241–4268, 2015. M. Caponigro, A. C. Lai, and B. Piccoli. A nonlinear model of opinion formation on the sphere. Discrete and Continuous Dynamical Systems Ser. A, (9):4241–4268, 2015.
17.
Zurück zum Zitat J. A. Carrillo, M. Fornasier, G. Toscani, and F. Vecil. Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, chapter Particle, kinetic, and hydrodynamic models of swarming, pages 297–336. Birkhäuser Boston, Boston, 2010. J. A. Carrillo, M. Fornasier, G. Toscani, and F. Vecil. Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, chapter Particle, kinetic, and hydrodynamic models of swarming, pages 297–336. Birkhäuser Boston, Boston, 2010.
18.
Zurück zum Zitat F. H. Clarke, Y. S. Ledyaev, E. D. Sontag, and A. I. Subbotin. Asymptotic controllability implies feedback stabilization. Automatic Control, IEEE Transactions on, 42(10):1394–1407, 1997.MathSciNetCrossRefMATH F. H. Clarke, Y. S. Ledyaev, E. D. Sontag, and A. I. Subbotin. Asymptotic controllability implies feedback stabilization. Automatic Control, IEEE Transactions on, 42(10):1394–1407, 1997.MathSciNetCrossRefMATH
19.
Zurück zum Zitat R. Colombo and N. Pogodaev. On the control of moving sets: positive and negative confinement results. SIAM J. Control Optim., 51(1):380–401, 2013.MathSciNetCrossRefMATH R. Colombo and N. Pogodaev. On the control of moving sets: positive and negative confinement results. SIAM J. Control Optim., 51(1):380–401, 2013.MathSciNetCrossRefMATH
20.
Zurück zum Zitat I. Couzin, J. Krause, R. James, G. Ruxton, and N. Franks. Collective memory and spatial sorting in animal groups. J Theor Biol, 218(1–11), 2002. I. Couzin, J. Krause, R. James, G. Ruxton, and N. Franks. Collective memory and spatial sorting in animal groups. J Theor Biol, 218(1–11), 2002.
21.
Zurück zum Zitat E. Cristiani, P. Frasca, and B. Piccoli. Effects of anisotropic interactions on the structure of animal groups. Journal of mathematical biology, 62(4):569–588, 2011.MathSciNetCrossRefMATH E. Cristiani, P. Frasca, and B. Piccoli. Effects of anisotropic interactions on the structure of animal groups. Journal of mathematical biology, 62(4):569–588, 2011.MathSciNetCrossRefMATH
22.
Zurück zum Zitat E. Cristiani, B. Piccoli, and C. Tosin. Multiscale modeling of granular flows with application to crowd dynamics. SIAM Multiscale Modeling and Simulations, 9:155–182, 2011.MathSciNetCrossRefMATH E. Cristiani, B. Piccoli, and C. Tosin. Multiscale modeling of granular flows with application to crowd dynamics. SIAM Multiscale Modeling and Simulations, 9:155–182, 2011.MathSciNetCrossRefMATH
23.
Zurück zum Zitat F. Cucker and S. Smale. Emergent behavior in flocks. IEEE Transactions on Automatic Control, 52:852–862, 2007.MathSciNetCrossRef F. Cucker and S. Smale. Emergent behavior in flocks. IEEE Transactions on Automatic Control, 52:852–862, 2007.MathSciNetCrossRef
24.
Zurück zum Zitat M. H. De Groot. Reaching a consensus. Journal of American Statistical Association, 69:118 – 121, 1974.CrossRefMATH M. H. De Groot. Reaching a consensus. Journal of American Statistical Association, 69:118 – 121, 1974.CrossRefMATH
25.
Zurück zum Zitat G. Deffuant, D. Neau, F. Amblard, and G. Weisbuch. Mixing beliefs among interacting agents. Advances in Complex Systems, 3(01n04):87–98, 2000. G. Deffuant, D. Neau, F. Amblard, and G. Weisbuch. Mixing beliefs among interacting agents. Advances in Complex Systems, 3(01n04):87–98, 2000.
26.
Zurück zum Zitat P. Degond, M. Herty, and J.-G. Liu. Mean-field games and model predictive control. preprint. P. Degond, M. Herty, and J.-G. Liu. Mean-field games and model predictive control. preprint.
27.
Zurück zum Zitat P. Degond, J.-G. Liu, and C. Ringhofer. Large-scale dynamics of mean-field games driven by local Nash equilibria. Journal of Nonlinear Science, 24(1):93–115, 2013.MathSciNetCrossRefMATH P. Degond, J.-G. Liu, and C. Ringhofer. Large-scale dynamics of mean-field games driven by local Nash equilibria. Journal of Nonlinear Science, 24(1):93–115, 2013.MathSciNetCrossRefMATH
28.
Zurück zum Zitat P. Degond and S. Motsch. Continuum limit of self-driven particles with orientation interaction. Mathematical Models and Methods in Applied Sciences, 18(supp01):1193–1215, 2008.MathSciNetCrossRefMATH P. Degond and S. Motsch. Continuum limit of self-driven particles with orientation interaction. Mathematical Models and Methods in Applied Sciences, 18(supp01):1193–1215, 2008.MathSciNetCrossRefMATH
29.
Zurück zum Zitat P. Degond and S. Motsch. Large scale dynamics of the persistent turning walker model of fish behavior. Journal of Statistical Physics, 131(6):989–1021, 2008.MathSciNetCrossRefMATH P. Degond and S. Motsch. Large scale dynamics of the persistent turning walker model of fish behavior. Journal of Statistical Physics, 131(6):989–1021, 2008.MathSciNetCrossRefMATH
30.
Zurück zum Zitat J. C. Dittmer. Diskrete nichtlineare modelle der konsensbildung. Diploma thesis Universität Bremen, 2000. J. C. Dittmer. Diskrete nichtlineare modelle der konsensbildung. Diploma thesis Universität Bremen, 2000.
31.
Zurück zum Zitat F. Dörfler, M. Chertkov, and F. Bullo. Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences, 110(6):2005–2010, 2013.MathSciNetCrossRefMATH F. Dörfler, M. Chertkov, and F. Bullo. Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences, 110(6):2005–2010, 2013.MathSciNetCrossRefMATH
32.
Zurück zum Zitat M. R. D’Orsogna, Y. L. Chuang, A. L. Bertozzi, and L. S. Chayes. Self-propelled particles with soft-core interactions: Patterns, stability, and collapse. Phys. Rev. Lett., 96:104302, Mar 2006. M. R. D’Orsogna, Y. L. Chuang, A. L. Bertozzi, and L. S. Chayes. Self-propelled particles with soft-core interactions: Patterns, stability, and collapse. Phys. Rev. Lett., 96:104302, Mar 2006.
33.
Zurück zum Zitat M. Fornasier, B. Piccoli, N. Pouradier Duteil, and F. Rossi. Mean-field optimal control by leaders. In 53rd IEEE Conference on Decision and Control, pages 6957–6962, Dec 2014. M. Fornasier, B. Piccoli, N. Pouradier Duteil, and F. Rossi. Mean-field optimal control by leaders. In 53rd IEEE Conference on Decision and Control, pages 6957–6962, Dec 2014.
34.
Zurück zum Zitat M. Fornasier, B. Piccoli, and F. Rossi. Mean-field sparse optimal control. Philosophilcal Transaction of the Royal Society A, 372, 2014. M. Fornasier, B. Piccoli, and F. Rossi. Mean-field sparse optimal control. Philosophilcal Transaction of the Royal Society A, 372, 2014.
35.
Zurück zum Zitat M. Fornasier and F. Solombrino. Mean-field optimal control. ESAIM: Control, Optimisation and Calculus of Variations, 20(4):1123–1152, 2014. M. Fornasier and F. Solombrino. Mean-field optimal control. ESAIM: Control, Optimisation and Calculus of Variations, 20(4):1123–1152, 2014.
36.
Zurück zum Zitat J. R. P. French. A formal theory of social power. Psychological Review, 63:181–194, 1956. J. R. P. French. A formal theory of social power. Psychological Review, 63:181–194, 1956.
37.
Zurück zum Zitat I. Giardina. Collective behavior in animal groups: theoretical models and empirical studies. Human Frontier Science Program Journal, (205–219), 2008. I. Giardina. Collective behavior in animal groups: theoretical models and empirical studies. Human Frontier Science Program Journal, (205–219), 2008.
38.
Zurück zum Zitat O. Guéant, J.-M. Lasry, and P.-L. Lions. Paris-Princeton Lectures on Mathematical Finance 2010, chapter Mean Field Games and Applications, pages 205–266. Springer Berlin Heidelberg, Berlin, Heidelberg, 2011. O. Guéant, J.-M. Lasry, and P.-L. Lions. Paris-Princeton Lectures on Mathematical Finance 2010, chapter Mean Field Games and Applications, pages 205–266. Springer Berlin Heidelberg, Berlin, Heidelberg, 2011.
39.
Zurück zum Zitat S. Y. Ha, T. Ha, and J. H. Kim. Emergent behavior of a Cucker–Smale type particle model with nonlinear velocity couplings. IEEE Transactions on Automatic Control, 55(7):1679–1683, July 2010. S. Y. Ha, T. Ha, and J. H. Kim. Emergent behavior of a Cucker–Smale type particle model with nonlinear velocity couplings. IEEE Transactions on Automatic Control, 55(7):1679–1683, July 2010.
40.
Zurück zum Zitat S.-Y. Ha, K. Lee, and D. Levy. Emergence of time-asymptotic flocking in a stochastic Cucker–Smale system. Commun. Math. Sci., 7(2):453–469, 06 2009. S.-Y. Ha, K. Lee, and D. Levy. Emergence of time-asymptotic flocking in a stochastic Cucker–Smale system. Commun. Math. Sci., 7(2):453–469, 06 2009.
41.
Zurück zum Zitat S.-Y. Ha and E. Tadmor. From particle to kinetic and hydrodynamic descriptions of flocking. arXiv preprint arXiv:0806.2182, 2008. S.-Y. Ha and E. Tadmor. From particle to kinetic and hydrodynamic descriptions of flocking. arXiv preprint arXiv:​0806.​2182, 2008.
42.
Zurück zum Zitat F. Harary. A criterion for unanimity in french’s theory of social power. Cartwright D (Ed.), Studies in Social Power, 1959. F. Harary. A criterion for unanimity in french’s theory of social power. Cartwright D (Ed.), Studies in Social Power, 1959.
43.
Zurück zum Zitat J. Haskovec. Flocking dynamics and mean-field limit in the Cucker–Smale-type model with topological interactions. Physica D: Nonlinear Phenomena, 261:42 – 51, 2013.MathSciNetCrossRefMATH J. Haskovec. Flocking dynamics and mean-field limit in the Cucker–Smale-type model with topological interactions. Physica D: Nonlinear Phenomena, 261:42 – 51, 2013.MathSciNetCrossRefMATH
44.
Zurück zum Zitat R. Hegselmann and A. Flache. Understanding complex social dynamics – a plea for cellular automata based modelling. Journal of Artificial Societies and Social Simulation, 1(3), 1998. R. Hegselmann and A. Flache. Understanding complex social dynamics – a plea for cellular automata based modelling. Journal of Artificial Societies and Social Simulation, 1(3), 1998.
45.
Zurück zum Zitat R. Hegselmann and U. Krause. Opinion dynamics and bounded confidence models, analysis, and simulation. Journal of Artificial Societies and Social Simulation, 5(3), 2002. R. Hegselmann and U. Krause. Opinion dynamics and bounded confidence models, analysis, and simulation. Journal of Artificial Societies and Social Simulation, 5(3), 2002.
46.
Zurück zum Zitat M. Herty, L. Pareschi, and S. Steffensen. Mean–field control and Riccati equations. Networks and Heterogeneous Media, 10(3):699–715, 2015.MathSciNetCrossRefMATH M. Herty, L. Pareschi, and S. Steffensen. Mean–field control and Riccati equations. Networks and Heterogeneous Media, 10(3):699–715, 2015.MathSciNetCrossRefMATH
47.
Zurück zum Zitat J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the national academy of sciences, 79(8):2554–2558, 1982.MathSciNetCrossRef J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the national academy of sciences, 79(8):2554–2558, 1982.MathSciNetCrossRef
48.
Zurück zum Zitat M. Huang, R. P. Malham, and P. E. Caines. Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst., 6(3):221–252, 2006.MathSciNetMATH M. Huang, R. P. Malham, and P. E. Caines. Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst., 6(3):221–252, 2006.MathSciNetMATH
49.
Zurück zum Zitat A. Huth and C. Wissel. The simulation of the movement of fish schools. Journal of Theoretical Biology, 156:365–385, 1992.CrossRef A. Huth and C. Wissel. The simulation of the movement of fish schools. Journal of Theoretical Biology, 156:365–385, 1992.CrossRef
50.
Zurück zum Zitat A. Isidori. Nonlinear control systems. Springer Science & Business Media, 2013. A. Isidori. Nonlinear control systems. Springer Science & Business Media, 2013.
51.
Zurück zum Zitat P. Jabin and S. Motsch. Clustering and asymptotic behavior in opinion formation. Journal of Differential Equations, 257(11):4165–4187, 12 2014. P. Jabin and S. Motsch. Clustering and asymptotic behavior in opinion formation. Journal of Differential Equations, 257(11):4165–4187, 12 2014.
52.
Zurück zum Zitat A. Jadbabaie, J. Lin, and A. S. Morse. Coordination of groups of mobile autonomous agents using nearest neighbor rules. Automatic Control, IEEE Transactions on, 48(6):988–1001, 2003.MathSciNetCrossRef A. Jadbabaie, J. Lin, and A. S. Morse. Coordination of groups of mobile autonomous agents using nearest neighbor rules. Automatic Control, IEEE Transactions on, 48(6):988–1001, 2003.MathSciNetCrossRef
53.
Zurück zum Zitat J. M. Kleinberg. Navigation in a small world. Nature, 406(6798):845–845, 08 2000. J. M. Kleinberg. Navigation in a small world. Nature, 406(6798):845–845, 08 2000.
54.
Zurück zum Zitat J. Krause and G. Ruxton. Living in groups. Oxford series in ecology and evolution. Oxford University Press, New York, 2002. J. Krause and G. Ruxton. Living in groups. Oxford series in ecology and evolution. Oxford University Press, New York, 2002.
55.
Zurück zum Zitat U. Krause. Soziale dynamiken mit vielen interakteuren, eine problemskizze. Krause U and Stöckler M (Eds.) Modellierung und Simulation von Dynamiken mit vielen interagierenden Akteuren, Universität Bremen, pages 37 – 51, 1997. U. Krause. Soziale dynamiken mit vielen interakteuren, eine problemskizze. Krause U and Stöckler M (Eds.) Modellierung und Simulation von Dynamiken mit vielen interagierenden Akteuren, Universität Bremen, pages 37 – 51, 1997.
56.
Zurück zum Zitat U. Krause. A discrete nonlinear and non—autonomous model of consensus formation. Elaydi S, Ladas G, Popenda J and Rakowski J (Eds.), Communications in Difference Equations, Amsterdam: Gordon and Breach Publ., pages 227 – 236, 2000. U. Krause. A discrete nonlinear and non—autonomous model of consensus formation. Elaydi S, Ladas G, Popenda J and Rakowski J (Eds.), Communications in Difference Equations, Amsterdam: Gordon and Breach Publ., pages 227 – 236, 2000.
57.
Zurück zum Zitat Y. Kuramoto. Cooperative dynamics of oscillator community a study based on lattice of rings. Progress of Theoretical Physics Supplement, 79:223–240, 1984.CrossRef Y. Kuramoto. Cooperative dynamics of oscillator community a study based on lattice of rings. Progress of Theoretical Physics Supplement, 79:223–240, 1984.CrossRef
58.
Zurück zum Zitat A. Lachapelle and M.-T. Wolfram. On a mean field game approach modeling congestion and aversion in pedestrian crowds. Transportation Research Part B: Methodological, 45(10):1572–1589, 2011.CrossRef A. Lachapelle and M.-T. Wolfram. On a mean field game approach modeling congestion and aversion in pedestrian crowds. Transportation Research Part B: Methodological, 45(10):1572–1589, 2011.CrossRef
60.
Zurück zum Zitat K. Lehrer. Social consensus and rational agnoiology. Synthese, 31:141 – 160, 1975.CrossRef K. Lehrer. Social consensus and rational agnoiology. Synthese, 31:141 – 160, 1975.CrossRef
61.
Zurück zum Zitat N. Leonard. Multi-agent system dynamics: Bifurcation and behavior of animal groups. Plenary paper IFAC Symposium on Nonlinear Control Systems, Toulouse, France., 2013. N. Leonard. Multi-agent system dynamics: Bifurcation and behavior of animal groups. Plenary paper IFAC Symposium on Nonlinear Control Systems, Toulouse, France., 2013.
62.
Zurück zum Zitat J. Maciejowski, P. Goulart, and E. Kerrigan. Constrained Control Using Model Predictive Control, pages 273–291. Springer Berlin Heidelberg, Berlin, Heidelberg, 2007. J. Maciejowski, P. Goulart, and E. Kerrigan. Constrained Control Using Model Predictive Control, pages 273–291. Springer Berlin Heidelberg, Berlin, Heidelberg, 2007.
63.
Zurück zum Zitat L. Moreau. Stability of continuous-time distributed consensus algorithms. In Decision and Control, 2004. CDC. 43rd IEEE Conference on, volume 4, pages 3998–4003. IEEE, 2004. L. Moreau. Stability of continuous-time distributed consensus algorithms. In Decision and Control, 2004. CDC. 43rd IEEE Conference on, volume 4, pages 3998–4003. IEEE, 2004.
64.
Zurück zum Zitat L. Moreau. Stability of multiagent systems with time-dependent communication links. Automatic Control, IEEE Transactions on, 50(2):169–182, 2005.MathSciNetCrossRef L. Moreau. Stability of multiagent systems with time-dependent communication links. Automatic Control, IEEE Transactions on, 50(2):169–182, 2005.MathSciNetCrossRef
66.
Zurück zum Zitat R. Olfati-Saber, J. A. Fax, and R. M. Murray. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 95(1):215–233, 2007.CrossRef R. Olfati-Saber, J. A. Fax, and R. M. Murray. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 95(1):215–233, 2007.CrossRef
67.
Zurück zum Zitat L. Pareschi and G. Toscani. Interacting multiagent systems: kinetic equations and Monte Carlo methods. OUP Oxford, 2013. L. Pareschi and G. Toscani. Interacting multiagent systems: kinetic equations and Monte Carlo methods. OUP Oxford, 2013.
68.
Zurück zum Zitat J. Parrish, S. Viscido, and D. Grunbaum. Self-organized fish schools: an examination of emergent properties. The Biological Bulletin, 202:296–305, 2002.CrossRef J. Parrish, S. Viscido, and D. Grunbaum. Self-organized fish schools: an examination of emergent properties. The Biological Bulletin, 202:296–305, 2002.CrossRef
69.
Zurück zum Zitat L. Perea, P. Elosegui, and G. Gómez. Extension of the Cucker–Smale control law to space flight formations. Journal of Guidance, Control, and Dynamics, 32:527–537, 2009.CrossRef L. Perea, P. Elosegui, and G. Gómez. Extension of the Cucker–Smale control law to space flight formations. Journal of Guidance, Control, and Dynamics, 32:527–537, 2009.CrossRef
70.
Zurück zum Zitat B. Piccoli, N. Pouradier Duteil, and B. Scharf. Optimal control of a collective migration model. Mathematical Models and Methods in Applied Sciences (to appear), 2015. B. Piccoli, N. Pouradier Duteil, and B. Scharf. Optimal control of a collective migration model. Mathematical Models and Methods in Applied Sciences (to appear), 2015.
71.
Zurück zum Zitat B. Piccoli, F. Rossi, and E. Trélat. Control to flocking of the kinetic Cucker–Smale model. SIAM Journal on Mathematical Analysis, 47(6):4685–4719, 2015.MathSciNetCrossRefMATH B. Piccoli, F. Rossi, and E. Trélat. Control to flocking of the kinetic Cucker–Smale model. SIAM Journal on Mathematical Analysis, 47(6):4685–4719, 2015.MathSciNetCrossRefMATH
72.
Zurück zum Zitat A. Rahmani, M. Ji, M. Mesbahi, and M. Egerstedt. Controllability of multi-agent systems from a graph-theoretic perpective. SIAM Journal on Control and Optimization, 48(1):162–186, 2009.MathSciNetCrossRefMATH A. Rahmani, M. Ji, M. Mesbahi, and M. Egerstedt. Controllability of multi-agent systems from a graph-theoretic perpective. SIAM Journal on Control and Optimization, 48(1):162–186, 2009.MathSciNetCrossRefMATH
73.
Zurück zum Zitat A. Sarlette. Geometry and symmetries in coordination control. PhD thesis, Université de Liège, 2009. A. Sarlette. Geometry and symmetries in coordination control. PhD thesis, Université de Liège, 2009.
74.
Zurück zum Zitat A. Sarlette and R. Sepulchre. Consensus optimization on manifolds. SIAM Journal on Control and Optimization, 48(1):56–76, 2009.MathSciNetCrossRefMATH A. Sarlette and R. Sepulchre. Consensus optimization on manifolds. SIAM Journal on Control and Optimization, 48(1):56–76, 2009.MathSciNetCrossRefMATH
75.
Zurück zum Zitat L. Scardovi, A. Sarlette, and R. Sepulchre. Synchronization and balancing on the N-torus. Systems & Control Letters, 56(5):335 – 341, 2007.MathSciNetCrossRefMATH L. Scardovi, A. Sarlette, and R. Sepulchre. Synchronization and balancing on the N-torus. Systems & Control Letters, 56(5):335 – 341, 2007.MathSciNetCrossRefMATH
76.
Zurück zum Zitat R. Sepulchre. Consensus on nonlinear spaces. Annual reviews in control, 35(1):56–64, 2011.CrossRefMATH R. Sepulchre. Consensus on nonlinear spaces. Annual reviews in control, 35(1):56–64, 2011.CrossRefMATH
77.
Zurück zum Zitat R. Sepulchre, D. Paley, N. E. Leonard, et al. Stabilization of planar collective motion: All-to-all communication. Automatic Control, IEEE Transactions on, 52(5):811–824, 2007.MathSciNetCrossRef R. Sepulchre, D. Paley, N. E. Leonard, et al. Stabilization of planar collective motion: All-to-all communication. Automatic Control, IEEE Transactions on, 52(5):811–824, 2007.MathSciNetCrossRef
78.
Zurück zum Zitat R. Sepulchre, D. Paley, N. E. Leonard, et al. Stabilization of planar collective motion with limited communication. Automatic Control, IEEE Transactions on, 53(3):706–719, 2008.MathSciNetCrossRef R. Sepulchre, D. Paley, N. E. Leonard, et al. Stabilization of planar collective motion with limited communication. Automatic Control, IEEE Transactions on, 53(3):706–719, 2008.MathSciNetCrossRef
79.
Zurück zum Zitat P. Sobkowicz. Modelling opinion formation with physics tools: Call for closer link with reality. Journal of Artificial Societies and Social Simulation, 12(1):11, 2009. P. Sobkowicz. Modelling opinion formation with physics tools: Call for closer link with reality. Journal of Artificial Societies and Social Simulation, 12(1):11, 2009.
80.
Zurück zum Zitat E. D. Sontag. Mathematical control theory: deterministic finite dimensional systems, volume 6. Springer Science & Business Media, 2013. E. D. Sontag. Mathematical control theory: deterministic finite dimensional systems, volume 6. Springer Science & Business Media, 2013.
81.
Zurück zum Zitat S. H. Strogatz. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D: Nonlinear Phenomena, 143(1–4):1 – 20, 2000.MathSciNetCrossRefMATH S. H. Strogatz. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D: Nonlinear Phenomena, 143(1–4):1 – 20, 2000.MathSciNetCrossRefMATH
82.
Zurück zum Zitat D. Sumpter. The principles of collective animal behaviour. Philosophilcal Transaction of the Royal Society B, 361:5–22, 2006.CrossRef D. Sumpter. The principles of collective animal behaviour. Philosophilcal Transaction of the Royal Society B, 361:5–22, 2006.CrossRef
83.
Zurück zum Zitat K. Sznajd-Weron and J. Sznajd. Opinion evolution in closed community. International Journal of Modern Physics C, 11(06):1157–1165, 2000.CrossRefMATH K. Sznajd-Weron and J. Sznajd. Opinion evolution in closed community. International Journal of Modern Physics C, 11(06):1157–1165, 2000.CrossRefMATH
84.
Zurück zum Zitat G. Toscani. Kinetic models of opinion formation. Commun. Math. Sci., 4(3):481–496, 09 2006. G. Toscani. Kinetic models of opinion formation. Commun. Math. Sci., 4(3):481–496, 09 2006.
85.
Zurück zum Zitat J. N. Tsitsiklis. Problems in Decentralized Decision making and Computation. PhD thesis, MIT, 1984. J. N. Tsitsiklis. Problems in Decentralized Decision making and Computation. PhD thesis, MIT, 1984.
86.
Zurück zum Zitat T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett., 75:1226–1229, Aug 1995.MathSciNetCrossRef T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett., 75:1226–1229, Aug 1995.MathSciNetCrossRef
87.
Zurück zum Zitat C. Villani. On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Archive for Rational Mechanics and Analysis, 143(3):273–307, 1998.MathSciNetCrossRefMATH C. Villani. On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Archive for Rational Mechanics and Analysis, 143(3):273–307, 1998.MathSciNetCrossRefMATH
88.
Zurück zum Zitat D. J. Watts and S. H. Strogatz. Collective dynamics of ‘small-world’ networks. Nature, 393(6684):440–442, 06 1998. D. J. Watts and S. H. Strogatz. Collective dynamics of ‘small-world’ networks. Nature, 393(6684):440–442, 06 1998.
89.
Zurück zum Zitat H. Whitney. On singularities of mappings of Euclidean spaces. I. mappings of the plane into the plane. Annals of Mathematics, 62(3):374–410, 1955.MathSciNetCrossRefMATH H. Whitney. On singularities of mappings of Euclidean spaces. I. mappings of the plane into the plane. Annals of Mathematics, 62(3):374–410, 1955.MathSciNetCrossRefMATH
90.
Zurück zum Zitat S. Wongkaew, M. Caponigro, and A. Borzi. On the control through leadership of the Hegselmann-Krause opinion formation model. Mathematical Models and Methods in Applied Sciences, 25(03):565–585, 2015.MathSciNetCrossRefMATH S. Wongkaew, M. Caponigro, and A. Borzi. On the control through leadership of the Hegselmann-Krause opinion formation model. Mathematical Models and Methods in Applied Sciences, 25(03):565–585, 2015.MathSciNetCrossRefMATH
91.
Zurück zum Zitat C. A. Yates, R. Erban, C. Escudero, I. D. Couzin, J. Buhl, I. G. Kevrekidis, P. K. Maini, and D. J. T. Sumpter. Inherent noise can facilitate coherence in collective swarm motion. Proceedings of the National Academy of Sciences, 106(14):5464–5469, 2009.CrossRef C. A. Yates, R. Erban, C. Escudero, I. D. Couzin, J. Buhl, I. G. Kevrekidis, P. K. Maini, and D. J. T. Sumpter. Inherent noise can facilitate coherence in collective swarm motion. Proceedings of the National Academy of Sciences, 106(14):5464–5469, 2009.CrossRef
Metadaten
Titel
Interaction Network, State Space, and Control in Social Dynamics
verfasst von
Aylin Aydoğdu
Marco Caponigro
Sean McQuade
Benedetto Piccoli
Nastassia Pouradier Duteil
Francesco Rossi
Emmanuel Trélat
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-49996-3_3

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