Time and place: Thursday, May 13, 11:40-12:10, 202 Chernoff Hall
Title: Adaptive Mean Field (NCE) Methodology in Leader-Follower
Stochastic Dynamic Games (½ hour)
Abstract: We consider an adaptive leader-follower dynamic games model
for large population systems . In this formulation the leaders track a
convex combination of their overall average together with a certain reference
trajectory which is unknown to the followers. The followers use a maximum
likelihood estimator (based on a fixed ratio sample of the population of the
leaders' trajectories) to identify the member of a given finite class of
models which is generating the reference trajectory of the leaders. We
approach this large population game problem by use of the so-called Mean
Field (Nash Certainty Equivalence) methodology [2,3,4]. Subject to
reasonable conditions the true reference trajectory model is identified in
finite time with probability one as the leaders' population goes to infinity
. Moreover, the system performance for the leaders is almost surely
optimal in the \epsilon-Nash sense and the system performance for the
adaptive followers is almost surely \epsilon-optimal with respect to the
 M. Nourian, P. E. Caines, R. P. Malhamé, and M. Huang,
"Leader-Follower maximum likelihood ratio adaptive NCE methodology,"
Technical Report, McGill University, April 2010.
 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:
 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.
 M. Huang, P. E. Caines, and R. P. Malhamé, "The NCE (Mean Field)
principle with locality dependent cost interactions," IEEE Transactions on
Automatic Control, to appear.
 M. Nourian, R.P. Malhamé, M. Huang, and P.E. Caines. "A mean field
(NCE) formulation of estimation based leader-follower collective
motion". International Journal of Robotics and Automation. (submitted
Aug. 2009; provisionally accepted Jan. 2010).
 M. Nourian, R.P. Malhamé, M. Huang, and P.E. Caines. "Optimality of
Adaption Based Mean Field (NCE) Control Laws in Leader-Follower Stochastic
Dynamic Games". submitted to 49th IEEE Conference on Decision and Control,
December 15-17, 2010, Atlanta, Georgia USA.