Derivation of consensus algorithm dynamics from mean field stochastic control NCE equations

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 1, Issue PART 1, 2009, Pages 13-18

  Nourian, Mojtaba ^a   Caines, Peter E ^a   Malhamé, Roland P ^b   Huang, Minyi ^c  

^a MCGILL UNIVERSITY   (Canada)

^b GERAD   (Canada)

^c CARLETON UNIVERSITY   (Canada)

Author keywords

Consensus problems; Coordinated control and estimation over networks; Decentralized and cooperativ e optimization

Indexed keywords

CERTAINTY EQUIVALENCE; CONSENSUS ALGORITHMS; CONSENSUS PROBLEMS; COORDINATED CONTROL AND ESTIMATION OVER NETWORKS; DECENTRALIZED AND COOPERATIV E OPTIMIZATION; DYNAMIC GAME; FINITE POPULATION; INITIAL STATE; LARGE POPULATION; LOCAL STATE FEEDBACK; MEAN FIELD; MEAN VALUES; NETWORK GRAPH; PRIORI INFORMATION; STOCHASTIC CONTROL;

ALGORITHMS; ESTIMATION; GAME THEORY; OPTIMIZATION; STATE FEEDBACK; STOCHASTIC CONTROL SYSTEMS;

STOCHASTIC SYSTEMS;

EID: 79960960552     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20090924-3-IT-4005.0019     Document Type: Conference Paper

References (17)

1. F. Cucker and E. Mordecki. Flocking in noisy environments. Journal de Mathématiques Pures et Appliqués, 89(3):278-296, 2008.
2. M. H. DeGroot. Reaching a consensus. Journal of the American Statistical Association, 69(345):118-121, 1974.
3. M. Huang and J. H. Manton. Coordination and consensus of networked agents with noisy measurements: Stochastic algorithms and asymptotic behavior. SIAM Journal on Control and Optimization, 48(1):134-161, 2009.
4. M. Huang, P. E. Caines, and R. P. Malhamé. Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized ε-Nash equilibria. IEEE Transactions on Automatic Control, 52(9):1560-1571, 2007. (Pubitemid 47456068)
5. M. Huang, P. E. Caines, and R. P. Malhamé. A locality generalization of the NCE (Mean Field) principle: Agent specific cost interactions. In Proceedings of the 47th IEEE Conference on Decision and Control, pages 5539-5544, Cancun, Mexico, December 2008.
6. M. Huang, P. E. Caines, and R. P. Malhamé. The NCE (Mean Field) principle with locality dependent cost interactions. Submitted to IEEE Transactions on Automatic Control, January 2009.
7. A. Jadbabaie, J. Lin, and A. S. Morse. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48(6):988-1001, 2003.
8. J. S. Krikorian. Contraction-mapping fixed-point theorem and finite-time stability. Electronics Letters, 5(7):157-158, 1969.
9. A. Lazarte. Large population stochastic dynamic games with nonuniform agents and localized coupling. Master's thesis, McGill University, Montreal, 2008.
10. T. Li. Asymptotically unbiased average consensus under measurement noises and fixed topologies. In Proceedings of the 17th World Congress, pages 2867-2873, Seoul, Korea, July 2008.
11. R. Olfati-Saber and R. M. Murray. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49: 1520-1533, 2004.
12. 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.
13. W. Ren, R. W. Beard, and E. M. Atkins. A survey of consensus problems in multi-agent coordination. In Proceedings of the American Control Conference, pages 1859-1864 vol. 3, Portland, USA, June 2005. (Pubitemid 41189135)
14. C. W. Reynolds. Flocks, herds, and schools: A distributed behavioral model. Computer Graphics, 21(4):25-34, 1987.
15. J. N. Tsistsiklis. Problems in decentralized decision making and computation. PhD thesis, MIT, 1984.
16. T. Vicsek, A. Czirók, E. B. Jacob, I. Cohen, and O. Shochet. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett., 75(6):1226-1229, 1995.
17. L. Xiao, S. Boyd, and S. J. Kim. Distributed average consensus with least-mean-square deviation. Journal of Parallel and Distributed Computing, 67(1):33-46, January 2007. (Pubitemid 44828440)