MEAN FIELD (NCE) FORMULATION OF ESTIMATION BASED LEADER–FOLLOWER COLLECTIVE DYNAMICS

Mojtaba Nourian, Roland P. Malhamé, Minyi Huang, and Peter E. Caines

References

  1. [1] M. Huang, R.P. Malhamé, & P.E. Caines, Stochastic powercontrol in wireless communication systems: Analysis, approx-imate control algorithms and state aggregation, 42nd IEEEConference on Decision and Control, Maui, HI, 2003,4231–4236.
  2. [2] Z. Lin, M. Broucke, & B. Francis, Local control strategies forgroups of mobile autonomous agents, IEEE Transactions onAutomatic Control, 49(4), 2004, 622–629.
  3. [3] J.A. Fax & R.M. Murray, Information flow and cooperativecontrol of vehicle formations, IEEE Transactions on AutomaticControl, 49(9), 2004, 1465–1476.
  4. [4] F. Cucker & S. Smale, Emergent behavior in flocks, IEEETransactions on Automatic Control, 52(5), 2007, 852–862.
  5. [5] V. Lambson, Self-enforcing collusion in large dynamic markets,Journal of Economic Theory, 34(2), 1984, 282–291.
  6. [6] C.M. Breder, Equations descriptive of fish schools and otheranimal aggregations, Ecology, 35(3), 1954, 361–370.
  7. [7] C.W. Reynolds, Flocks, herds, and schools: A distributedbehavioral model, Computer Graphics, 21(4), 1987, 25–34.127
  8. [8] S.A. Levin, Complex adaptive systems: Exploring the known,the unknown and the unknowable, Bulletin-American Mathe-matical Society, 40(1), 2003, 3–20.
  9. [9] J. Krause, D. Hoare, S. Krause, C.K. Hemelrijk, & D.I.Rubenstein, Leadership in fish shoals, Fish and Fisheries, 1,2000, 82–89.
  10. [10] D. Lusseau, Evidence for social role in a dolphin social network,Evolutionary Ecology, 21(3), 2007, 357–366.
  11. [11] I.D. Couzin, J. Krause, N.R. Franks, & S.A. Levin, Effectiveleadership and decision-making in animal groups on the move,Nature, 433, 2005, 513–516.
  12. [12] M. Huang, P.E. Caines, & R.P. Malhamé, Large-populationcost-coupled LQG problems with nonuniform agents:Individual-mass behavior and decentralized -Nash equilibria,IEEE Transactions on Automatic Control, 52(9), 2007, 1560–1571.
  13. [13] M. Huang, P.E. Caines, & R.P. Malhamé, The NCE (meanfield) principle with locality dependent cost interactions, Toappear in IEEE Transactions on Automatic Control, 2010.
  14. [14] M. Huang, R.P. Malhamé, & P.E. Caines, Nash equilibria forlarge-population linear stochastic systems of weakly coupledagents, in Analysis, Control and Optimization of ComplexDynamic Systems (GERAD 25th Annivesary Series), E.K.Boukas and R.P. Malhame (Eds.), 2005, 215–252.
  15. [15] M. Huang, Large-population LQG games involving a majorplayer: the Nash certainty equivalence principle, SIAM Journalon Control and Optimization, 48(5), 2010, 3318–3353.
  16. [16] M. Huang, R.P. Malhamé, & P.E. Caines, Large populationstochastic dynamic games: closed-loop Mckean-Vlasov systemsand the Nash certainty equivalence principle, Communicationsin Information and Systems, 6(3), 2006, 221–252.
  17. [17] T. Li & J.F. Zhang, Asymptotically optimal decentralizedcontrol for large population stochastic multiagent systems,IEEE Transactions on Automatic Control, 53(7), 2008, 1643–1660.
  18. [18] M. Nourian, P.E. Caines, R.P. Malhamé, & M. Huang,Derivation of consensus algorithm dynamics from mean-field stochastic control NCE equations, Proc. of 1st IFACWorkshop on Estimation and Control of Networked Sys-tems (NecSys09), Venice, Italy, 2009. http://www.ifac-papersonline.net/Detailed/40520.html.
  19. [19] J.M. Lasry & P.L. Lions, Mean field games, Japanese Journalof Mathematics, 2(1), 2007, 229–260.
  20. [20] G.Y. Weintraub, C.L. Benkard, & B. Van Roy, Oblivious equilibrium: a mean field approximation for large-scale dynamicgames, Advances in Neural Information Processing Systems(MIT Press, 2005).
  21. [21] Z. Qu, Cooperative control of dynamical systems: Applicationsto autonomous vehicles, (London: Springer, 2009).
  22. [22] M. Nourian, R.P. Malhamé, M. Huang, & P.E. Caines, Adaptivemean field control in leader-follower stochastic dynamic games,Technical Report, McGill University, 2010.
  23. [23] http://www.pond5.com/stock-footage/286251/school-of-sardines-circling.html.
  24. [24] P.E. Caines, Linear stochastic systems, (New York, NY: JohnWiley & Sons, 1987).
  25. [25] G.C. Goodwin & K.S. Sin, Adaptive filtering prediction andcontrol, (Englewood Cliffs, NJ: Prentice-Hall, 1984).
  26. [26] F.L. Lewis, Optimal estimation: With an introduction tostochastic control theory, (New York: John Wiley and Sons,1986).
  27. [27] P.E. Caines, A note on the consistency of maximum likelihoodestimates for finite families of stochastic processes, The Annalsof Statistics, 3(2), 1975, 539–546.
  28. [28] T. Duncan, Evaluation of likelihood functions, Informationand Control, 13(1), 1968, 62–74.

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