Learning in mean-field oscillator games

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2010, Pages 3125-3132

  Yin, Huibing ^a   Mehta, Prashant G ^a   Meyn, Sean P ^a   Shanbhag, Uday V ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; CONTROL THEORY; GALERKIN METHODS; MICROWAVE OSCILLATORS; OSCILLATORS (MECHANICAL); STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS; SYNCHRONIZATION;

APPROXIMATE DYNAMIC PROGRAMMING; COUPLED OSCILLATORS; GALERKIN APPROXIMATIONS; NONCOOPERATIVE DYNAMIC GAMES; NUMERICAL EXPERIMENTS; ON-LINE ALGORITHMS; OPTIMAL CONTROL LAW; STOCHASTIC APPROXIMATION ALGORITHMS;

DYNAMIC PROGRAMMING;

EID: 79953147145     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2010.5717142     Document Type: Conference Paper

References (10)

1. H. Yin, P. G. Mehta, S. P. Meyn, and U. V. Shanbhag, " Synchronization of coupled oscillators is a game," in Proc. of 2010 American Control Conference, Baltimore, MD, 2010, pp. 1783-1790. [Online]. Available: http://mechse.illinois.edu/media/uploads/web sites/67/files/sync game ymms.20100124.4b5d050d77dc00.29251135.pdf
2. Y. Kuramoto, "Self-entrainment of a population of coupled nonlinear oscillators," In H. Araki, editor, International Symposium on Mathematical Problems in Theoretical Physics, vol. 39, p. 420, 1975, ser. Lecture Notes in Physics, Springer.
3. M. Huang, P. E. Caines, and R. P. Malhame, "Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized ε-Nash equilibria," IEEE Trans. Automat. Control, vol. 52, no. 9, pp. 1560-1571, 2007.
4. G. Y. Weintraub, L. Benkard, and B. V. Roy, "Oblivious equilibrium: A mean field approximation for large-scale dynamic games," in Advances in Neural Information Processing Systems, vol. 18. MIT Press, 2006.
5. M. Steriade, D. A. McCormick, and T. J. Sejnowski, "Thalamocortical Oscillations in the Sleeping and Aroused Brain," Science, vol. 262, pp. 679-685, Oct. 1993.
6. D. Bertsekas and J. N. Tsitsiklis, Neuro-Dynamic Programming. Cambridge, Mass: Atena Scientific, 1996.
7. P. G. Mehta and S. P. Meyn, "Q-learning and Pontryagin's Minimum Principle," in Proc. of 48th IEEE Conference on Decision and Control, December 2009, pp. 3598-3603.
8. S. H. Strogatz and R. E. Mirollo, "Stability of incoherence in a population of coupled oscillators," Journal of Statistical Physics, vol. 63, pp. 613-635, May 1991.
9. H. Kielhöfer, Bifurcation Theory. An Introduction with Applications to PDEs, ser. Applied Mathematical Sciences. Springer, 2003, no. 156.
10. V. S. Borkar and S. P. Meyn, "The ODE method for convergence of stochastic approximation and reinforcement learning," SIAM J. Control Optim., vol. 38, no. 2, pp. 447-469, 2000.