Sparse stabilization of dynamical systems driven by attraction and avoidance forces

Networks and Heterogeneous Media

Volumn 9, Issue 1, 2014, Pages 1-31

  Bongini, Mattia ^a   Fornasier, Massimo ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Cohesion and avoidance forces; Consensus emergence; L1 norm minimization; Optimal control with ODE constraints; Sparse stabilization

Indexed keywords

DYNAMICAL SYSTEMS; FEEDBACK CONTROL; OPTIMIZATION; STABILIZATION;

COHESION AND AVOIDANCE FORCES; CONSENSUS EMERGENCE; CRITICAL THRESHOLD; DECENTRALIZED FEEDBACK; L1-NORM MINIMIZATIONS; OPTIMAL CONTROLS; STABLE CONFIGURATION; STABLE ENERGY LEVELS;

EMBEDDED SYSTEMS;

EID: 84898872919     PISSN: 15561801     EISSN: 1556181X     Source Type: Journal    
DOI: 10.3934/nhm.2014.9.1     Document Type: Article

References (24)

1. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Clarendon Press, Oxford University Press, New York, 2000.
2. J.-P. Aubin and A. Cellina, Differential Inclusions, Set-valued maps and viability theory, Grundlehren der Mathematischen Wissenschaften, 264, Springer-Verlag, Berlin, 1984.
3. M. Caponigro, M. Fornasier, B. Piccoli and E. Trélat, Sparse stabilization and control of alignment models, Math. Control Relat. Fields, 3 (2013), 447-466. Available from: http: //www-m15.ma.tum.de/foswiki/pub/M15/Allgemeines/PublicationsEN/flocking_V9.pdf.
4. J. A. Carrillo, Y.-P. Choi and M. Hauray, The derivation of swarming models: Mean-field limit and Wasserstein distances, in Collective Dynamics from Bacteria to Crowds, CISM International Centre for Mechanical Sciences, 553, Springer, 2014, 1-46.
5. J. A. Carrillo, M. R. D'Orsogna and V. Panferov, Double milling in self-propelled swarms from kinetic theory, Kinet. Relat. Models, 2 (2009), 363-378.
6. J. A. Carrillo, M. Fornasier, G. Toscani and F. Vecil, Particle, kinetic, and hydrodynamic models of swarming, 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.
7. Y. Chuang, M. D'Orsogna, D. Marthaler, A. Bertozzi and L. Chayes, State transition and the continuum limit for the 2D interacting, self-propelled particle system, Physica D, 232 (2007), 33-47.
8. F. Cucker and J.-G. Dong, A general collision-avoiding ocking framework, IEEE Trans. Automat. Control, 56 (2011), 1124-1129.
9. F. Cucker and J.-G. Dong, A conditional, collision-avoiding, model for swarming, Discrete and Continuous Dynamical Systems, 34 (2014), 1009-1020.
10. F. Cucker and S. Smale, Emergent behavior in ocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
11. F. Cucker and S. Smale, On the mathematics of emergence, Jpn. J. Math., 2 (2007), 197-227.
12. M. D'Orsogna, Y. Chuang, A. Bertozzi and L. Chayes, Self-propelled particles with soft-core interactions: Patterns, stability, and collapse, Phys. Rev. Lett., 96 (2006).
13. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, Translated from the Russian, Mathematics and its Applications (Soviet Series), 18, Kluwer Academic Publishers Group, Dordrecht, 1988.
14. M. Fornasier and F. Solombrino, Mean-field optimal control, preprint, arXiv:1306.5913, (2013).
15. S.-Y. Ha, T. Ha and J.-H. Kim, Emergent behavior of a Cucker-Smale type particle model with nonlinear velocity couplings, IEEE Trans. Automat. Control, 55 (2010), 1679-1683.
16. J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, 1998.
17. M. Huang, P. Caines and R. Malhamé, Individual and mass behaviour in large population stochastic wireless power control problems: Centralized and nash equilibrium solutions, in Proceedings of the 42nd IEEE Conference on Decision and Control Maui, Hawaii, USA, December, 2003, 98-103.
18. J.-M. Lasry and P.-L. Lions, Mean field games, Jpn. J. Math. (3), 2 (2007), 229-260.
19. S. Motsch and E. Tadmor, Heterophilious dynamics enhances consensus, SIAM Rev., to appear.
20. M. Nuorian, P. Caines and R. Malhamé, Synthesis of Cucker-Smale type ocking via mean field stochastic control theory: Nash equilibria, in Proceedings of the 48th Allerton Conf. on Comm., Cont. and Comp., Monticello, Illinois, 2010, 814-819.
21. M. Nuorian, P. Caines and R. Malhamé, Mean field analysis of controlled Cucker-Smale type flocking: Linear analysis and perturbation equations, in Proceedings of 18th IFAC World Congress Milano (Italy) August 28-September 2, 2011, 4471-4476.
22. A. Rahmani, M. Ji, M. Mesbahi and M. Egerstedt, Controllability of multi-agent systems from a graph-theoretic perspective, SIAM J. Control and Optimization, 48 (2009), 162-186.
23. H. G. Tanner, On the controllability of nearest neighbor interconnections, in Proceedings of the 43rd IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, 2004, 2467-2472.
24. T. Vicsek and A. Zafeiris, Collective motion, Physics Reports, 517 (2012), 71-140.