Titre:
A Mathematical Foundation for Adaptation, Learning, Discovery, and Invention in Nonlinear Dynamical Systems
Conférencier:
Rui J.P. de Figueiredo ,
University of California, Irvine, É.-U.
Lieu:
Université Concordia, SGW Campus, EV003.309 ,
Date et heure:
mercredi le 01 avril 2009 de
18:00 à 19:30
Résumé:
The processes of adaptation, learning, discovery, and invention are expected to play an increasingly significant role in emerging large-scale computationally intelligent (CI) systems. The meanings of “adaptation” and “learning” are well-known. By “discovery” we mean the process of creating a new hypothesis based on sufficient new data that does not fit existing hypotheses, while by “invention”, the process of creating (synthesizing) new prototypes by interpolation or extrapolation of existing ones.
In this lecture we will present a kernel-based mathematical approach to the modeling and design of the processes of adaptation, learning, discovery and invention in nonlinear dynamical systems. The approach is based on our previous work in which uncertainty is handled by mathematical approximation theory methods, specifically, by best approximation of nonlinear functionals in an appropriate Reproducing Kernel Hilbert Space (RKHS). This formulation leads to optimal nonlinear system models in the form of artificial neural networks (ANNs) in a natural way, that is, without imposing, a-priori, a neural structure on the system being modeled. For this reason, while connecting with the mathematical foundations on which they are based, we will use ANNs as generic representations of the nonlinear dynamical systems under discussion. Computer simulation results, some using real data, will be presented to establish and illustrate the theoretical developments.
Note biographique: Rui J. P. de Figueiredo, B.S. and M.S. (Electrical Engineering), M.I.T., and Ph.D. (Applied Mathematics), Harvard University, is Research Professor (Above Scale) of Electrical Engineering and Computer Science and Mathematics, at the University of California, Irvine (UCI). He is also Director of the Laboratory for Intelligent Signal Processing and Communications in the California Institute for Telecommunications and Information Technology of UCI. Prior to joining UCI in 1990, Dr. de Figueiredo served as Professor of Electrical Engineering and Mathematical Sciences at Rice University, Houston, Texas (1965-90). Professor de Figueiredo has won numerous honors for his fundamental contributions to the theory and applications of signal/image processing and communications, and to nonlinear control; and for his role as an educator and as a leader in his field and in his profession. These honors include: election to the UN-sponsored International Informatization Academy (2003), election to the Russian Academy of Natural Sciences in 2007 and Academy’s George V Chilinger Medal of Honor, the 1999 IEEE Circuits and Systems (CAS) Society Golden Jubilee Medal, the 2000 IEEE Tri-Millennium Medal, the 2003 Gh. Asachi Medal from the Technical University of Iasi (TUI), Romania, from which he also received the title of Honorary Professor (2003), the IEEE Fellow Award (1976), the 1994 IEEE CAS Technical Achievement Award, the 2000 IEEE Neural Networks Transactions Best Paper Award, the 2003 IEEE Circuits and Systems Transactions Guillemin-Cauer Best Paper Award, the 2002 IEEE CAS Society M. E. Van Valkenburg Society Award, the 1988 NCR Educator-of-the-Year Award, his election to President of IEEE CAS Society in 1998, and, last but not least, his selection by IEEE to be one of its fifty leaders, among its nearly 350,000 members, to present the IEEE vision of the new century in the book ENGINEERING TOMORROW: Today’s Technology Experts Envision the Next Century, Janie Fouke, Editor, IEEE Press, 2000.