
Time and place: Thursday, May 13, 11:4012:10, 202 Chernoff Hall
Title: Adaptive Mean Field (NCE) Methodology in LeaderFollower
Stochastic Dynamic Games (½ hour)
Abstract: We consider an adaptive leaderfollower dynamic games model
for large population systems [1]. 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 socalled 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
[5]. Moreover, the system performance for the leaders is almost surely
optimal in the \epsilonNash sense and the system performance for the
adaptive followers is almost surely \epsilonoptimal with respect to the
leaders [6].
References:
[1] M. Nourian, P. E. Caines, R. P. Malhamé, and M. Huang,
"LeaderFollower maximum likelihood ratio adaptive NCE methodology,"
Technical Report, McGill University, April 2010.
[2] 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:
http://www.ieeecss.org/CAB/conferences/cdc2009/shanghai2009.31.pdf
[3] M. Huang, P. E. Caines, and R. P. Malhamé, "Largepopulation
costcoupled LQG problems with nonuniform agents: Individualmass behavior
and decentralized eNash equilibria," IEEE Transactions on Automatic
Control, vol. 52, no. 9, pp. 1560~ 1571, 2007.
[4] 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.
[5] M. Nourian, R.P. Malhamé, M. Huang, and P.E. Caines. "A mean field
(NCE) formulation of estimation based leaderfollower collective
motion". International Journal of Robotics and Automation. (submitted
Aug. 2009; provisionally accepted Jan. 2010).
[6] M. Nourian, R.P. Malhamé, M. Huang, and P.E. Caines. "Optimality of
Adaption Based Mean Field (NCE) Control Laws in LeaderFollower Stochastic
Dynamic Games". submitted to 49th IEEE Conference on Decision and Control,
December 1517, 2010, Atlanta, Georgia USA.
