Synchronization of coupled oscillators is a game

Proceedings of the 2010 American Control Conference, ACC 2010

Volumn , Issue , 2010, Pages 1783-1790

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

^a United States of America   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION ANALYSIS; CONTROL COSTS; COUPLED OSCILLATORS; CRITICAL VALUE; DYNAMIC GAME; DYNAMICAL SYSTEMS THEORY; ENGINEERING APPLICATIONS; LARGE POPULATION; NASH EQUILIBRIUM; NON-HOMOGENEOUS; NONLINEAR COST FUNCTIONS; NUMERICAL EXPERIMENTS; PDE MODEL; PHASE ANGLES; POPULATION SIZES; STOCHASTIC DIFFERENTIAL EQUATION MODELS;

BIFURCATION (MATHEMATICS); DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS; NONLINEAR EQUATIONS; OSCILLATORS (ELECTRONIC); OSCILLATORS (MECHANICAL); PHASE TRANSITIONS; POPULATION STATISTICS; STOCHASTIC SYSTEMS;

STOCHASTIC MODELS;

EID: 77957788593     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (16)

1. S. Adlakha, R. Johari, G. Y. Weintraub, and A. J. Goldsmith. Oblivious equilibrium for large-scale stochastic games with unbounded costs. In Proc. of the 47th IEEE Conf. On Decision and Control, pages 5531- 5538, Cancun, Mexico, dec 2008.
2. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang. Spectral Methods in Fluid Dynamics. Springer-Verlag, 1988.
3. R. Cogill, M. Rotkowitz, B. Van Roy, and S. Lall. An approximate dynamic programming approach to decentralized control of stochastic systems. In Proceedings of the 2004 Allerton Conference on Communication, Control, and Computing, pages 1040-1049, 2004.
4. M. Dellnitz, J.E. Marsden, I. Melbourne, and J. Scheurle. Generic bifurcations of pendula. Int. Series Num. Math., 104:111-122, 1992.
5. V. F. Farias, D. Saure, and G. Y. Weintraub. The linear programming approach to solving large scale dynamic stochastic games (working paper). http://www.stanford.edu/bvr/publ-all.html, 2008.
6. 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, 52(9):1560-1571, 2007.
7. Y. Kuramoto. International Symposium on Mathematical Problems in Theoretical Physics, volume 39 of Lecture Notes in Physics. Springer-Verlag, 1975.
8. T. Li and J.-F. Zhang. Asymptotically optimal decentralized control for large population stochastic multiagent systems. IEEE Trans. Automat. Control, 53(7):1643-1660, 2008.
9. P. Mehta and S. Meyn. Q-learning and Pontryagin's Minimum Principle. Accepted for inclusion in the 48th IEEE Conference on Decision and Control, December 16-18 2009.
10. S. P. Meyn. The policy iteration algorithm for average reward Markov decision processes with general state space. IEEE Trans. Automat. Control, 42(12):1663-1680, 1997.
11. S. P. Meyn and G. Mathew. Shannon meets Bellman: Feature based Markovian models for detection and optimization. In Proc. 47th IEEE CDC, pages 5558-5564, 2008.
12. A. W. Naylor and G. R. Sell. Linear Operator Theory in Engineering and Science, volume 40 of Applied Mathematical Sciences. Springer-Verlag, 1982.
13. M. Steriade, D. A. McCormick, and T. J. Sejnowski. Thalamocortical Oscillations in the Sleeping and Aroused Brain. Science, 262:679-685, October 1993.
14. S. H. Strogatz and R. E. Mirollo. Stability of incoherence in a population of coupled oscillators. Journal of Statistical Physics, 63:613-635, May 1991.
15. M. von Krosigk, T. Bal, and D. A. McCormick. Cellular mechanisms of a synchronized oscillation in the thalamus. Science, 261:361-364, 1993.
16. G. Y. Weintraub, L. Benkard, and B. Van Roy. Oblivious equilibrium: A mean field approximation for large-scale dynamic games. In Advances in Neural Information Processing Systems, volume 18. MIT Press, 2006.