January 27, 2012, Webb 1100

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.

Ian Manchester was born in 1979 in Sydney, Australia. He received the BE (Hons 1) 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.