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Synchronization of Oscillators as a Feedback Stabilization Problem

Synchronization of Oscillators as a Feedback Stabilization Problem

Dr. Roger Brockett
Harvard University
Speaker: Dr. Roger Brockett, Harvard University

Monday, March 2, 2015  |  11:00 AM CST

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Abstract

Synchronization of oscillations is essential to the operation of many communication and control systems and has been studied in various contexts since the middle of the 17th century. Phase-locked loops, electrical power networks and oscillations responsible for various biological processes are common examples requiring high accuracy.  However, in contrast to the problem of using feedback control to achieve asymptotic stability of an equilibrium point, the mechanisms available to achieve an asymptotically stable periodic solution are much more limited.  In this talk we frame the question of synchronization as a feedback stabilization problem and precisely identify the possible mechanisms which can lead to perfect steady state synchronization.  In the process we will clarify the relationship between controllability and the feedback stabilization of oscillations.


Biography

Roger Brockett is the An Wang Research Professor of Electrical Engineering and Computer Science in the School of Engineering and Applied Sciences at Harvard University. He received his B.S., M.S. and Ph.D. degrees from Case Western Reserve University and taught for six years in the Electrical Engineering Department at MIT before joining the Harvard faculty in 1969. He retired from the teaching faculty in 2012.

Dr. Brockett has contributed to the theory of automatic control with work on stability, nonlinear control, feedback linearization, nonlinear estimation, pole placement, hybrid systems, and robotics. More recently his work has involved problems arising in the study of intelligent machines. Areas of particular interest include the problem of motion control, minimum attention control, synchronization and the investigation of new paradigms in quantum control.

Dr. Brockett has been recognized with awards from the American Automatic Control Council, IEEE, ASME and SIAM for his contributions to research and education. He is a fellow of the IEEE, SIAM, and AMS and is a member of the US National Academy of Engineering.