Location: 118 Auditorium, Technology Square Research Building
George Yin
Professor
Department of Mathematics
University of Connecticut
Abstract
In this talk, we will present some of our recent work on stochastic Kolmogorov systems. The motivation stems from dealing with important issues of ecological and biological systems. Focusing on environmental noise, we aim to address such fundamental questions: “what are the minimal conditions for long-term persistence of a population, or long-term coexistence of interacting species”. Some optimal control problems are also examined. [The talk reports some of our joint works with D.H. Nguyen, N.T. Dieu, N.H. Du, and N.N Nguyen.]
Biography
George Yin received the B.S. degree in mathematics from the University of Delaware in 1983, and the M.S. degree in electrical engineering and the Ph.D. degree in applied mathematics from BrownUniversity in 1987. He joined the Department of Mathematics, Wayne State University in 1987 and became Professor in 1996 and University Distinguished Professor in 2017. He moved to the University of Connecticut in 2020. His research interests include stochastic processes, stochastic systems theory, and applications. He was Chair of the SIAM Activity Group on Control and Systems Theory, and was Co-chair of a number of conferences; he served on the Board of Directors of the American Automatic Control Council. He is Editor-in-Chief of SIAM Journal on Control and Optimization. He serves on (or served on) editorial boards of over 20 journals and book series including Automatica 1995-2011, IEEE Transactions on Automatic Control 1994-1998, and IEEE Control Systems Letters 2017-2019. He is a Fellow of IEEE, Fellow of IFAC, and Fellow of SIAM.
W. Grafton and Lillian B. Wilkins Professor of Mechanical Science and Engineering at UIUC.
Abstract
Learning-based control paradigms have seen many success stories with various robots and co-robots in recent years. However, as these robots prepare to enter the real world, operating safely in the presence of imperfect model knowledge and external disturbances is going to be vital to ensure mission success. In the first part of the talk, we present an overview of L1 adaptive control, how it enables safety in autonomous robots, and discuss some of its success stories in the aerospace industry. In the second part of the talk, we present some of our recent results that explore various architectures with L1 adaptive control while guaranteeing performance and robustness throughout the learning process. An overview of different projects at our lab that build upon this framework will be demonstrated to show different applications.
Biography
Naira Hovakimyan received her MS degree in Theoretical Mechanics and Applied Mathematics in 1988 from Yerevan State University in Armenia. She got her Ph.D. in Physics and Mathematics in 1992 from the Institute of Applied Mathematics of Russian Academy of Sciences in Moscow. She is currently a W. Grafton and Lillian B. Wilkins Professor of Mechanical Science and Engineering at UIUC. In 2015 she was named inaugural director for Intelligent Robotics Lab of Coordinated Science Laboratory at UIUC. She has co-authored two books, eleven patents and more than 450 refereed publications. She was the recipient of the SICE International scholarship for the best paper of a young investigator in the VII ISDG Symposium (Japan, 1996), the 2011 recipient of AIAA Mechanics and Control of FlightAward, the 2015 recipient of SWE Achievement Award, the 2017 recipient of IEEE CSS Award for Technical Excellence in Aerospace Controls, and the 2019recipient of AIAA Pendray Aerospace Literature Award. In 2014 she was awarded the Humboldt prize for her lifetime achievements. She is Fellow and life member of AIAA and a Fellow of IEEE. She is cofounder and chief scientist of IntelinAir. Her work in robotics for elderly care was featured in the New York Times, on Fox TV and CNBC. Her research interests are in control, estimation and optimization, autonomous systems, game theory and their broad applications across various industries.
This talk will give an overview of old and new results and directions in stochastic approximation algorithms, broadly split into basic theory, variants, and applications. Central to all this will be the ‘o.d.e’ (for ‘Ordinary Differential Equations’) approach to their analysis.
Biography
Prof. Vivek S. Borkar is CSIR Bhatnagar Emeritus Fellow at Indian Institute of Technology Bombay. He obtained his B.Tech. (EE) from IIT Bombay, M.S. (Systems and Control) from Case Western Reserve Uni., and Ph.D. (EECS) from the Uni. of California, Berkeley, in 1976, 77, 80 resp. He has held positions in TIFR Centre and Indian Institute of Science, Bengaluru, and Tata Inst. of Fundamental Research and IIT Bombay in Mumbai. He is a Fellow of IEEE, AMS, TWAS and various science and engineering academies in India. He was awarded the S. S. Bhatnagar Prize in engineering sciences by the Government of India in 1992 and was an invited speaker at the International Congress of Mathematicians in Madrid in 2006. His research interests are in stochastic control and optimization, inclusive of theory, algorithms, and applications, particularly to communications.
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. This leads, under some structural constraints, to what is known as mean field games (MFGs), which have been the subject of intense research activity during the last ten years or so.
MFGs constitute a class of non-cooperative stochastic differential games where there is a large number of players or agents who interact with each other through a mean field coupling term—also known as the mass behavior or the macroscopic behavior in statistical physics—included in the individual cost functions and/or each agent’s dynamics generated by a controlled stochastic differential equation, capturing the average behavior of all agents. One of the main research issues in MFGs with no hierarchy in decision making is to study the existence, uniqueness and characterization of Nash equilibria with an infinite population of players under specified information structures and further to study finite-population approximations, that is to explore to what extent an infinite-population Nash equilibrium provides an approximate Nash equilibrium for the finite-population game, and what the relationship is between the level of approximation and the size of the population.
Following a general overview of the difficulties brought about by strategic interactions in finite-population SDGs, the talk will dwell on two classes of MFGs: those characterized by risk sensitive (that is, exponentiated) objective functions (known as risk-sensitive MFGs) and those that have risk-neutral (RN) objective functions but with an additional adversarial driving term in the dynamics (known as robust MFGs). In stochastic optimal control, it is known that risk-sensitive (RS) cost functions lead to a behavior akin to robustness, leading to establishment of a connection between RS control problems and RN minimax ones. The talk will explore to what extent a similar connection holds between RS MFGs and robust MFGs, particularly in the context of linear-quadratic problems, which will allow for closed-form solutions and explicit comparisons between the two in both infinite- and finite-population regimes and with respect to the approximation of Nash equilibria in going from the former to the latter. The talk will conclude with a brief discussion of several extensions of the framework, such as to hierarchical decision structures with a small number of players at the top of the hierarchy (leaders) and an infinite population of agents at the bottom (followers) as well as to games where players make noisy observations.
Biography
Tamer BaÅŸar has been with the University of Illinois at Urbana-Champaign since 1981, where he holds the academic positions of Swanlund Endowed Chair; Center for Advanced Study (CAS) Professor of Electrical and Computer Engineering; Professor, Coordinated Science Laboratory; Professor, Information Trust Institute; and Affiliate Professor, Mechanical Science and Engineering. He is also the Director of the Center for Advanced Study. At Illinois, he has also served as Interim Dean of Engineering and Interim Director of the Beckman Institute for Advanced Science and Technology. He is a member of the US National Academy of Engineering; Fellow of IEEE, IFAC, and SIAM; a past president of the IEEE Control Systems Society (CSS), the founding president of the International Society of Dynamic Games (ISDG), and a past president of 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, and a number of international honorary doctorates and professorships, most recently an honorary doctorate from KTH, Sweden. He has over 900 publications in systems, control, communications, optimization, networks, and dynamic games, including books on non-cooperative dynamic game theory, robust control, network security, wireless and communication networks, and stochastic networks. He was Editor-in-Chief of the IFAC Journal Automatica between 2004 and 2014, and is currently editor of several book series. His current research interests include stochastic teams, games, and networks; multi-agent systems and learning; data-driven distributed optimization; epidemics modeling and control over networks; security and trust; energy systems; and cyber-physical systems.
