Optimality of adaption based mean field control laws in leader-follower stochastic collective dynamics

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2010, Pages 2270-2275

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

^a MCGILL UNIVERSITY   (Canada)

^b GERAD   (Canada)

^c CARLETON UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL THEORY; NAVIGATION; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TRAJECTORIES;

CERTAINTY EQUIVALENCE; COLLECTIVE DYNAMICS; CONVEX COMBINATIONS; LEADER-FOLLOWER; MAXIMUM LIKELIHOOD ESTIMATOR; MAXIMUM LIKELIHOOD RATIOS; NASH EQUILIBRIA; REFERENCE TRAJECTORIES;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 79953141437     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2010.5717537     Document Type: Conference Paper

References (19)

1. M. Huang, R. P. Malhamé, and P. E. Caines, "Stochastic power control in wireless communication systems: analysis, approximate control algorithms and state aggregation," in 42nd IEEE Conference on Decision and Control, Maui, HI, December 2003, pp. 4231-4236.
2. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988-1001, 2003.
3. L. Perea, G. Gómez, and P. Elosegui, "Extension of the Cucker-Smale control law to space flight formations," Journal of Guidance, Control, and Dynamics, vol. 32, no. 2, pp. 527-537, 2009.
4. V. Lambson, "Self-enforcing collusion in large dynamic markets," Journal of Economic Theory, vol. 34, no. 2, pp. 282-291, 1984.
5. G. Y. Weintraub, C. L. Benkard, and B. Van Roy, "Markov perfect industry dynamics with many firms," Social Science Research Network Working Paper Series, February 2006.
6. J. R. G. Dyer, A. Johansson, D. Helbing, I. D. Couzin, and J. Krause, "Leadership, consensus decision making and collective behaviour in humans," Philosophical Transactions of the Royal Society B: Biolog- ical Sciences, vol. 364, no. 1518, pp. 781-789, March 2009.
7. I. D. Couzin, J. Krause, N. R. Franks, and S. A. Levin, "Effective leadership and decision-making in animal groups on the move," Nature, vol. 433, no. 7025, pp. 513-516, February 2005.
8. M. Simaan and J. Cruz, "On the Stackelberg strategy in nonzero-sum games," Journal of Optimization Theory and Applications, vol. 11, no. 5, pp. 533-555, 1973.
9. W. Wang and J. E. Slotine, "A theoretical study of different leader roles in networks," IEEE Transactions on Automatic Control, vol. 51, no. 7, pp. 1156-1161, 2006.
10. D. Gu and Z. Wang, "Leader - follower flocking: algorithms and experiments," IEEE Transactions on Control Systems Technology, vol. 17, no. 5, pp. 1211-1219, 2009.
11. M. Nourian, R. P. Malhamé, M. Huang, and P. E. Caines, "Mean field (NCE) formulation of estimation based leader-follower collective dynamics," International Journal of Robotics and Automation, Special Issue on New Advances in Nonlinear and Optimal Controls of Robotic and Autonomous Systems, to appear.
12. M. Nourian, P. E. Caines, R. P. Malhamé, and M. Huang, "Adaptive mean field control in leader-follower stochastic dynamic games," IEEE Transactions on Automatic Control, submitted.
13. P. E. Caines, "Bode lecture: Mean Field stochastic control," Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, December, 2009. [Online]. Available: http://www.ieeecss.org/CAB/ conferences/cdc2009/shanghai2009.31.pdf
14. M. Huang, R. P. Malhamé, and P. E. Caines, "Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions," in 42th IEEE Conference on Decision and Control, Hawaii, December 2003, pp. 98-103.
15. M. Huang, P. E. Caines, and R. P. Malhamé, "Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized e -Nash equilibria," IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1560-1571, 2007.
16. -, "The NCE (Mean Field) principle with locality dependent cost interactions," IEEE Transactions on Automatic Control, to appear, 2010.
17. T. Li and J. F. Zhang, "Asymptotically optimal decentralized control for large population stochastic multiagent systems," IEEE Transactions on Automatic Control, vol. 53, no. 7, pp. 1643-1660, 2008.
18. T. Duncan, "Evaluation of likelihood functions," Information and Control, vol. 13, no. 1, pp. 62-74, July 1968.
19. P. E. Caines, "A note on the consistency of maximum likelihood estimates for finite families of stochastic processes," The Annals of Statistics, vol. 3, no. 2, pp. 539-546, 1975.