Unstable Systems Stabilizing Each Other through Adaptation: How Do We Learn from Each Other
Abstract: An asymptotically stable reference model plays a crucial role in the entire literature on adaptive systems. Given a plant with unknown parameters, the objective is to adjust the parameters of a controller so that the behavior of the controlled plant emulates that of the reference model. The existence of a stable reference model is not assured in all situations. Such problems are arising with increasing frequency in various disciplines such as biology, psychology, economics, and robotics. This lecture will address the following question which is markedly different from that encountered in conventional adaptive control “Can two or more unstable adaptive systems stabilize each other through adaptation?” Two interacting nth order adaptive systems give rise to nonlinear stability problems in a 4n dimensional space which are truly formidable. Necessary and sufficient conditions for the stability of such systems are currently unknown. The lecture will describe the theoretical insights provided by extensive simulation studies and the theoretical analysis of special cases suggested by them.
Speaker's Bio: Kumpati Narendra is currently the Harold W. Cheel Professor of Electrical Engineering and the Director of the Center for System Science at Yale University. He received his Ph.D degree from Harvard University and was an Assistant Professor there until 1965, when he came to Yale. He was made Professor in 1968. He was the Chairman of the Electrical Engineering Department from 1984 to 1987 and the Director of the NeuroEngineering and NeuroScience Center during 1995-96. Professor Narendra is the author of over 250 papers and 3 books and the editor of 4 books in the fields of Adaptive Control, Learning Theory, Stability Theory and Neural Networks. He has delivered over 100 lectures in 45 countries and has mentored 47 PhD students and 38 postdoctoral and visiting fellows in the past 40 years. During the same period he was a consultant for over 15 industrial research laboratories, including General Motors, AT&T, Sikorsky Aircraft, Schlumberger, and Sandia National Laboratories. Professor Narendra is a Fellow of the IEEE, the IEE, Sigma Xi, and the American Association for the Advancement of Science. He received numerous awards in the past, including the Richard E. Bellman Control Heritage Award, the highest award of the American Automatic Control Council (AACC), for Pioneering Contributions to Stability Theory, and Adaptive and Learning Theory.