Seminars of the Focus Area Complex Systems

Prof. Dr. C. Beta, Prof. Dr. K. Dethloff, Prof. Dr. R. Engbert, Prof. Dr. M. Holschneider, Prof. Dr. W. Huisinga, Prof. Dr. Ralf Metzler, Prof. Dr. A. Pikovsky, Prof. Dr. S. Reich, Prof. Dr. M. Rosenblum, Prof. Dr. G. Rüdiger, Prof. Dr. T. Scheffer, Prof. Dr. F. Scherbaum, Prof. Dr. J. Selbig, Prof. Dr. F. Spahn


Speaker: Prashant Mehta , University of Illinois at Urbana-Champaign, USA

Title: Phase transition in mean-field games: An application to synchronization of coupled oscillators * SFB 1294 seminar

Time: Mon, Aug 28, 2017, 2pm

Place: bldg 9, room 0.14

This talk is concerned with phase transition and self-organization in mean-field games. The motivation comes from the following sequence of events that transpired on June 10, 2000 when a bridge opened in London to mark the dawn of the new millennium. As the citizens of London poured on to the Millennium bridge, it quickly became apparent that there was a problem. In the words of Pat Dallard of Arup Corporation, the firm responsible for bridge design, “We were witnessing the bridge performing in a way that we hadn't anticipated ... We felt that we understood it very well and here it is doing something completely unexpected.”

The unexpected behavior of the bridge (shown using a you-tube video at the beginning of my talk) is an example of rational irrationality: even when the behavior of an individual (pedestrian on the bridge) is rational from the individual's perspective, the resulting collective behavior (of the crowd) may be irrational from the group’s perspective. The technical contents of the talk will revolve around a game-theoretic variant of the classical Kuramoto coupled-oscillator model. The main conclusion is that the synchronization of the coupled oscillators can be obtained as a solution of a mean-field game whereby the classical Kuramoto control law is an approximation of the game-theoretic solution.

This is joint work with Huibing Yin, Sean Meyn and Uday Shanbhag:

1. Yin, H., P. G. Mehta, S. P. Meyn and U. V. Shanbhag, “Synchronization of Coupled Oscillators is a Game," IEEE Transactions on Automatic Control, 57:4, 920-935, April 2012.

2. Yin, H., P. G. Mehta, S. P. Meyn and U. V. Shanbhag, “Learning in Mean-field Games," IEEE Transactions on Automatic Control, 59:3, 629-644, March 2014.

3. Yin, H., P. G. Mehta, S. P. Meyn and U. V. Shanbhag, “On the Efficiency of Equilibria in Mean-field Oscillator Games," Journal of Dynamic Games and Applications, 4:2, 177-207, June 2014.

Biography: Prashant Mehta is an Associate Professor in the Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign. He received his Ph.D. in Applied Mathematics from Cornell University in 2004. Prior to joining Illinois, he was a Research Engineer at the United Technologies Research Center (UTRC). His research interests are at the intersection of dynamical systems and control theory, including nonlinear filtering, mean-field games, model reduction, and nonlinear control. Prashant Mehta received the Outstanding Achievement Award at UTRC for his contributions to modeling and control of combustion instabilities in jet-engines. His students received the Best Student Paper Awards at the IEEE Conference on Decision and Control 2007 and 2009 and were finalists for these awards in 2010 and 2012. He has served on the editorial boards of the ASME Journal of Dynamic Systems, Measurement, and Control and the Systems and Control Letters.

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