November 14, 2014, Roger Brockett, CISE Resident Scholar, Harvard University
Friday, November 14, 2014 at 3:00 PM to 4:00 PM
8 St. Mary’s Street, Room 210
Refreshments served at 2:45.
Synchronization: Minimal Complexity Models for Zero Steady State Synchronization Error
We will present a model for synchronization of families of second order oscillators which is truly dynamical, not just based on simplified phase dynamics, as well as being robust in the sense that the steady state error goes to zero, independent of the precise strength of the coupling terms.
Mathematically speaking, questions about synchronization are usually thought of as questions about the stability properties of a one dimensional manifold, “the oscillation”. We pose the synchronization problem as a stabilization problem in which the target is a one-dimensional manifold, not just a point. Splitting the problem up as a part which supports (not synchronized) oscillations and a feedback mechanism which brings about synchronization is helpful because we can then treat the problem in pieces.
Roger Brockett is An Wang research professor of Electrical Engineering and Computer Science at Harvard University. He was a student at Case Institute of Technology and did his Ph.D. work under the supervision of Mihajlo D. Mesarovic, in the Systems Research Center then led by Donald P. Eckman. Prior to joining the Harvard faculty in 1969, he taught for six years in the Electrical Engineering department at MIT, where he developed the textbook Finite Dimensional Linear Systems and involved graduate students in a range of topics centering on stability theory and applications. At Harvard, working along side of Y.C. Ho and an outstanding group of younger colleagues, he initially focused on the theory and applications of nonlinear systems emphasizing the use of differential geometric ideas. In the mid 1980s, fostered in part by the new NSF Engineering Research Center imitative and the ARO MURI program administered by Jagdish Chandra, the focus of his research turned to the application of control theoretic ideas to problems in robotics, computer vision and other aspects of intelligent machines. An important part of this transition was the development of a broadly inclusive robotics laboratory, engaging a number of Harvard faculty members as well as involving, long-term collaborations with colleagues and former students at Brown University, the University of Maryland, and MIT. His teaching has involved the development of courses for engineering students, ranging from a freshman design course to graduate level teaching across the field of control. In many cases his former Ph.D. students and post doctoral researchers have gone on to become leaders in their fields with their accomplishments being recognized, not only because of their work in their “day jobs” as teachers, researchers and managers, but also through their contributions to the management and editorial work of various IEEE societies, SIAM journals, etc.
Faculty Host: John Baillieul
Student Host: Fatme Yanikara