Abstract Perhaps the most challenging aspect of research on multi-agent dynamical systems, formulated as non-cooperative stochastic differential/dynamic games (SDGs) with asymmetric dynamic information structures, is the presence of strategic interactions among agents, with each one developing beliefs on others in the absence of shared information. This belief generation process involves what is known as second-guessing phenomenon, which generally entails infinite recursions, thus compounding the difficulty of obtaining (and arriving at) an equilibrium. This difficulty is somewhat alleviated when there is a high population of agents (players), in which case strategic interactions at the level of each agent become much less pronounced. With some structural specifications, this leads to what is known as mean field games (MFGs), which have been the subject of intense research activity during the last fifteen years or so.
The talk will first provide a general overview of fundamentals of MFGs approach to decision making in multi-agent dynamical systems in both model-based and model-free settings, and discuss connections to finite-population games. Following this general introduction, the talk will focus, for concrete results, on the structured setting of discrete-time infinite-horizon linearquadratic-Gaussian dynamic games, where the players are partitioned into finitely-many populations with an underlying graph topology---a framework motivated by paradigms where consensus and dissensus co-exist. In this formulation, each population has a high number of indistinguishable agents, but there is no indistinguishability across different populations. It is possible to characterize the Nash equilibrium (NE) of the underlying game when the number of agents in each population goes to infinity, the so-called mean-field equilibrium (MFE), with only local state information for each agent, which can then be shown to lead to an approximate NE when the population sizes are finite, with a precise quantification of the approximation as a function of population sizes. For the model-free versions of such games, a reinforcement learning algorithm will be introduced based on zero-order stochastic optimization, for computation of the MFE, along with guaranteed convergence. The talk will also address derivation of a finite-sample bound, quantifying the estimation error as a function of the number of samples, and will conclude with a discussion of some extensions of the general setting and future research directions.
Tamer Basar has been with University of Illinois Urbana-Champaign since 1981, where he is currently Swanlund Endowed Chair Emeritus; CAS Professor Emeritus of ECE; and Research Professor, CSL and ITI. He has served as Director of the Center for Advanced Study (2014-2020), Interim Dean of Engineering (2018), and Interim Director of the Beckman Institute (2008-2010). He is a member of the US National Academy of Engineering; Fellow of IEEE, IFAC, and SIAM; and has served as presidents of the IEEE Control Systems Society (CSS), the International Society of Dynamic Games (ISDG), and the American Automatic Control Council (AACC). He has received several awards and recognitions over the years, including the highest awards of IEEE CSS, IFAC, AACC, and ISDG, the IEEE Control Systems Technical Field Award, Wilbur Cross Medal from his alma mater Yale, and a number of international honorary doctorates and professorships. He was Editor-in-Chief of the IFAC Journal Automatica between 2004 and 2014, and is currently editor of several book series. He has contributed profusely to fields of systems, control, communications, optimization, networks, and dynamic games, and has current research interests in stochastic teams, games, and networks; multi-agent systems and learning; data-driven distributed optimization; epidemics modeling and control over networks; strategic information transmission, spread of disinformation, and deception; security and trust; energy systems; and cyber-physical systems
Abstract Network systems are mathematical models for the study of cooperation, propagation, synchronization and other dynamical phenomena that arise among interconnected agents. Network systems are widespread in science as they are fundamental modeling tools, e.g., in sociology and epidemiology. They also play a key growing role in technology, e.g., in the design of power grids, cooperative robotic behaviors and distributed computing algorithms. Their study pervades applied mathematics.
This talk will review established and emerging frameworks for modeling, analysis and design of network systems. I will survey the available comprehensive theory for linear network systems and then highlight selected nonlinear concepts. Next, I will focus on recent developments by my group on a rigorous and comprehensive framework for the analysis of security, transmission capacity, and multistability for active power flow in power networks.
Francesco Bullo is a Professor in the Mechanical Engineering Department at the University of California, Santa Barbara. He received the Laurea degree “summa cum laude” in Electrical Engineering from the University of Padova, Italy, in 1994, and the Ph.D. degree in Control and Dynamical Systems from the California Institute of Technology in 1999. From 1998 to 2004, he was an Assistant Professor with the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign. Since 2004 he has been at University of California, Santa Barbara; he is currently affiliated with the Department of Electrical and Computer Engineering, the Department of Computer Science, and the Center for Control, Dynamical Systems and Computation. His research interests focus on network systems and distributed control with application to robotic coordination, power grids and social networks. He is the coauthor of “Geometric Control of Mechanical Systems” (Springer, 2004) and “Distributed Control of Robotic Networks” (Princeton, 2009); his “Lectures on Network Systems” (CreateSpace, 2018) is available on his website. Professor Bullo is a Fellow of IEEE and IFAC. He is currently a Distinguished Lecturer of the IEEE Control Systems Society. He received the 2018 Distinguished Scientist Award by the Chinese Academy of Sciences. His articles received the 2008 CSM Outstanding Paper Award from IEEE CSS, the 2011 Hugo Schuck Best Paper Award from AACC, the 2013 SIAG/CST Best Paper Prize from SIAM, the 2014 Automatica Best Paper Prize from IFAC, the 2016 Guillemin-Cauer Best Paper Award from IEEE CAS, and the 2016 TCNS Outstanding Paper Award from IEEE CSS. Professor Bullo served as advisor or co-advisor of 22 graduated PhD students. He received the 2015 UCSB Outstanding Graduate Mentor Award and the 2004 UIUC COE Outstanding Advisor Award. His students’ papers were finalists for the Best Student Paper Award at the IEEE Conference on Decision and Control (2002, 2005, 2007), and the American Control Conference (2005, 2006, 2010). Professor Bullo has served, for the IEEE Control Systems Society, as 2011-2012 Vice-President for Technical Activities, as 2013-2014 Vice-President for Publications, as 2007-2009 Elected Member of the Board of Governors and as Program Chair for the 2016 IEEE Conference in Decision and Control. He is serving as President Elect / President / President Past of the IEEE Control Systems Society during the triennium 2017–2019. Additionally, he served on the Editorial Boards of “IEEE Transactions on Automatic Control,” “ESAIM: Control, Optimization, and the Calculus of Variations,” “SIAM Journal of Control and Optimization,” and “Mathematics of Control, Signals, and Systems”.
Abstract Our motivation for the research to be described is derived from the following fact: The expected value of a random variable X, denoted E(X), is often inconsistent with what human beings may actually expect based on psychological considerations. This is particularly important when predictions involving life-threatening situations arise.
To bring this issue into sharp focus, this seminar begins with a set of questions related to the recent rampage of Hurricane Irma from the Gulf of Mexico into in the State of Florida. When the use of empirical data leads to an expected value forecast of storm surge wave height which is unduly pessimistic, will the “boy who cried wolf” effect be in play the next time a hurricane approaches the mainland? On the other hand, if the formally calculated expected wave height is too optimistic, might it be the case that many will take inadequate protective measures? Based on such considerations, we define a new alternative to E(X) which we believe is quite useful for “mission critical” situations with downside risk being of paramount concern. We call this new metric the Conservative Expected Value and denote it by CEV(X). In this talk, we provide the technical definition of the CEV, compare it with the classical expected value and describe some aspects of the rich mathematical theory which accompanies it. We also include a description of some of the studies we have conducted using the CEV to evaluate historical data. This talk is dedicated to the memory of Roberto Tempo.
B. Ross Barmish is Professor of Electrical and Computer Engineering at the University of Wisconsin, Madison. Prior to joining UW in 1984, he held faculty positions at Yale University and the University of Rochester. From 2001-2003, he served as Chair of the EECS Department at Case Western Reserve while holding the Nord endowed professorship. He received his Bachelor’s degree in EE from McGill University and the M.S. and Ph.D. degrees, also in EE, from Cornell University.
Throughout his career, he has served the IEEE Control Systems Society in many capacities and has been a consultant for a number of companies. Professor Barmish is the author of the textbook “New Tools for Robustness of Linear Systems” and is a Fellow of both the IEEE and IFAC for his contributions to robust control. He received two Best Journal Publication awards, each covering a three-year period, from the International Federation of Automatic Control and has given a number of keynotes and plenary lectures at major conferences. In 2013, he received the IEEE Control Systems Society Bode Prize.
While his earlier work concentrated on robustness of dynamical systems, his current university research involves building a bridge between feedback control theory and trading in complex financial markets. In addition to this academic pursuit, in his capacity as CEO of Robust Trading Solutions, his work involves transition of stock-trading algorithms from theory to practice and government sponsored research on the NASDAQ Limit Order Book.