数学与系统科学研究院学术报告

报告题目：Mean Field Stochastic Control: Egoists, Altruists and Flocking Synthesis

报 告 人：Peter E. Caines，McGill University

时间地点：10：00-11：00，AM，July 19, Room 703, Siyuan Building

摘要：

For noncooperative stochastic dynamic games, the Nash CertaintyEquivalence (NCE), or Mean Field (MF), methodology (Huang, Caines,Malham\'e, 2003 CDC, 2007 TAC, etc) provides decentralized strategieswhich asymptotically in population size generate Nash equilibria formasses of egoistic agents.

Egoists and Altruists: An extension of this theory to populations ofaltruistic agents (defined with so-called social cost functions) and henceto mixed egoist-altruist populations has been carried out by Huang, Cainesand Malham\'e (2010 CDC). The equilibria and the stability of the dynamicLQG game problems is considered for large populations of mixed agents forwhich the cost for each minor agent is a convex combination of its owncost and the social cost of the population of minor agents, as measured byan ``egoism degree $\lambda$''. When applied to mixed populations wherethere is also a major agent (as in the theory developed by Huang (2010SICOPT)), Mean Field stochastic control algorithms give rise to behaviourswhere (Kizilkale, Caines, 2011): (i) all agents systems are $L^2$ stable,(ii) all agents are in $\epsilon$-Nash equilibrium, (iii) if each minoragent in the system only considers the social cost, the differencebetween the cost incurred for each minor agent and the (per head) socialcost incurred by a centralized social cost minimizing controller tends tozero as the population size goes to infinity, and (iv) there is a simplesensitivity function for the agent behaviours with respect to the egoismdegree $\lambda$. Finally, (v) conjectures concerning the formation andstability of coalitions are derived.

Flocking Synthesis: In this model of Cucker-Smale (C-S) type flockingthe state of each individual agent consists of both its position and itscontrolled velocity, and all agents have similar stochastic dynamics. Theagents are coupled via their nonlinear individual cost functions which arebased on the C-S flocking algorithm in its original uncontrolledformulation. The MF continuum system of equations approximates thisstochastic system of individual agents as the population size tends toinfinity. The key result (Nourian, Caines, Malham\'e, 2011) is that C-Sflocking behaviour may be obtained as a dynamic Nash equilibrium. Afteranalyzing the case of linear cost coupling, we present the perturbed(i.e., linearized) equations of the nonlinear MF system and giveconditions for non-Gaussian initial conditions to give rise to $L^2$stable trajectories with respect to the stationary Gaussian solutions.

报告人简介：

Peter E. Caines received the BA in mathematics from OxfordUniversity in 1967 and the PhD in systems and control theory in 1970 from ImperialCollege, University of London. After periods as a postdoctoral researcher and faculty member at UMIST, Stanford, UC Berkeley, Toronto and Harvard, he joined McGillUniversity, Montreal, in 1980, where he is James McGill Professor and MacDonald Chair in the Department of Electrical and Computer Engineering.

He is a Fellow of the IEEE, SIAM and the Canadian Institute for Advanced Research, and was elected to the Royal Society of Canada in 2003. In 2009, he received the IEEE Control Systems Society Bode Lecture, which is one of the highest awards in the control systems community of the world.

He has served as an Associate Editor of the IEEE Trans. on Automatic Control, the IEEE Trans. on Information Theory and the SIAM Journal on Control andOptimization; during 1992-1995 he served on the Board of Governors of the IEEE Control Systems Society, was a Member of the Scientific Advisory Board of the Max Plank Society, 2002--2007 and the EU HYCON Review Committee, 2005--2007. He is the author of Linear Stochastic Systems, John Wiley, 1988, and is the co-editor of several volumes of papers on stochastic systems.

His research interests include the areas of system identification, adaptive control, logic control and discrete event systems. Recently his activities have focused on hybrid systems theory, and stochastic multi-agent and distributed systems theory, together with their links to physics, economics and biology.