Control and Dynamical Lecture Series: Prashant Mehta, "Phase Transition in Large Population Games"
Thursday, March 4, 2010
2460 A.V. Williams Building
301 405 6576
Phase transition in large population games: An application to synchronization of coupled oscillators
Coordinated Science Laboratory
Dept. of Mechanical Science & Engineering
University of Illinois at Urbana-Champaign
This talk is concerned with phase transition in non-cooperative dynamic games with a large number of nonlinear agents.
The talk is motivated by problems at the intersection of game theory and nonlinear dynamical systems. Game theory provides a powerful set of tools for analysis and design of strategic behavior in controlled multi-agent systems. In economics, for example, game-theoretic techniques provide a foundation for analyzing the behavior of rational agents in markets. In practice, a fundamental problem is that controlled multi-agent systems can exhibit phase transitions with often undesirable outcomes. In economics, an example of this is the so-called rational irrationality.
A prototypical example of multi-agent system that exhibits phase transition is the coupled oscillator model of Kuramoto. In this talk, a variant of the Kuramoto model is used albeit in a novel game-theoretic setting for control. The main conclusion is that the synchronization of the coupled oscillators can be interpreted as a solution of a non-cooperative dynamic game. The classical Kuramoto control law can be obtained as an approximation of the game-theoretic solution. Approximate dynamic programming techniques to obtain the Kuramoto control law are discussed.
This is joint work with Sean Meyn and Uday Shanbhag at the University of Illinois.
Prashant Mehta is an Assistant Professor at 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 UIUC, 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 fundamental limitations in nonlinear control, model reduction of Markov chains, phase transition and learning in large population games.
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 Award at the IEEE Conference on Decision and Control 2007 and 2009.