**
Peter Caines, ECE, McGill University, Montreal**

Webb Hall 1100

The central notion of Mean Field (MF) (or Nash Certainty Equivalence (NCE)) stochastic control theory is that for general classes of large population stochastic dynamic games there exist Nash equilibria for the individual agents when each applies certain competitive strategies. In this work each agent is modelled by an individually controlled stochastic system and the systems interact through their individual cost functions and possibly via weak dynamical interaction. The crucial feedback nature of the MF control laws is that the optimal individual competitive actions against the mass behaviour act so as to collectively reproduce that mass behaviour (a xed point property), and hence the equilibrium is stable in the Nash game theoretic sense. The Nash equilibria and associated feedback control laws are precomputable in the innite population case via the NCE Equation schemes and yield approximate equilibria when applied in the nite population case.

In this talk the basic formulation of Mean Field stochastic control theory and its adaptive generalization will rst be presented; then two new topics will be introduced: (i) a continuum based MF approach to the consensus problem, and (ii) the MF control of populations where there are both major (i.e. massive) agents and mixed populations of egoist-altruist agents.

Work with M.Y. Huang, R.P. Malhame, A.C. Kizilkale and M. Nourian.

**About Peter Caines:**

Peter Caines received the BA in mathematics from Oxford University in 1967 and the PhD in systems and control theory in 1970 from Imperial College,University of London, under the supervision of David Q. Mayne, FRS. After periods as a postdoctoral researcher and faculty member at UMIST, Stanford, UC Berkeley, Toronto and Harvard, he joined McGill University, Montreal, in 1980, where he is James McGill Professor and Macdonald Chair in the Department of Electrical and Computer Engineering. Peter Caines is a Fellow of the IEEE, SIAM and the Canadian Institute for Advanced Research, was elected to the Royal Society of Canada in 2003 and received the IEEE Control Systems Society Bode Lecture Prize in 2009; he is the author of Linear Stochastic Systems, John Wiley, 1988, and his research interests include stochastic, multi-agent and hybrid systems theory together with their links to physics, economics and biology.

**Hosted by: CCDC Seminar, host: Bassam Bamieh**