Ian Manchester, Jan 2012

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Ian Manchester will visit CDS on 25 Jan 2012 (Wed). If you would like to meet with him, please sign up below.

  • 12:30pm-2:00pm: Lunch and discussion; please sign up here if you want to join the lunch

meet at west gate of second floor @ Annenberg, outside classroom 213

  • 2:00-3:00pm: Talk @ CDS library
  • 3:00-3:30: Necmiye (maybe chat @ CDS tea)
  • 3:30-4:00: Dom
  • 4:00-4:30: Eric + Ufuk
  • 4:30-5:00: open
  • 5:00-5:30: open

Identification and Analysis of Nonlinear Oscillations via Convex Relaxation

Ian Machester
MIT

Abstract: Stable and self-sustained oscillations (aka limit cycles) are an intriguing dynamical phenomenon: they are ubiquitous in natural and engineered systems; they are the second thing anyone looks for (after equilibria) when analyzing a dynamic system; and yet they cause great difficulty for many familiar concepts from systems and control. Stable oscillation is an inherently nonlinear phenomenon. Trajectories live on the "edge of stability", i.e. they always have one critically stable Lyapunov exponent and cannot be asymptotically stable in the usual sense. Their regions of attraction can never be all of R^n but are always "donut shaped".

This talk will cover some recent work on control, analysis, and identification for systems with limit cycles. We will derive computationally tractable methods using transverse coordinates, convex relaxations, and semidefinite/sum-of-squares programming. The main examples covered will be region-of-stability analysis for an underactuated walking robot, and black-box system identification of live neurons in culture.

Biography

Ian Manchester received the BE and PhD degrees in Electrical Engineering from the University of New South Wales, Sydney. He was then a post-doc and guest lecturer at Umeå University, Sweden. He is presently a Research Scientist with the Robot Locomotion Group, Massachusetts Institute of Technology. For the last 2 yrs he was working with Alex Megretski and Russ Tedrake, mostly on convex optimization algorithms for nonlinear system identification and analysis. A particular focus has been identifying and analyzing systems with autonomous oscillations (limit cycles) including live neurons in culture, and walking robots.