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Global Stability Analysis of Fluid Flows using Sum-of-Squares

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Abstract:
This talk will describe a new method for assessing the stability of fluid flows governed by the Navier-Stokes equations. Finite-dimensional approximations to the Navier-Stokes equations typically take the form of a set of linear ODEs with an additional nonlinear term that conserves the total energy of the system state. A method for computing Lyapunov functions using sum-of-squares optimization that exploits this energy conservation property will be developed for the finite dimensional case. It will then be shown how these sum-of-squares methods can be applied to infinite dimensional fluid systems via robust optimization.

Type of Seminar:
IfA Internal Seminar
Speaker:
Dr. Paul Goulart
Department of Aeronautics, Imperial College
Date/Time:
Nov 19, 2010   11.00
Location:

ETF C 109
Contact Person:

Manfred Morari
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Biographical Sketch:
Paul Goulart is a lecturer in control systems in the Department of Aeronautics at Imperial College London. He received BSc and MSc degrees in Aeronautics and Astronautics from the Massachusetts Institute of Technology (MIT). He was selected as a Gates Scholar at the University of Cambridge, where he received a PhD in Control Engineering in 2007. From 1998 to 2002 he was an engineer in the Flight Operations Group of the Chandra X-Ray Observatory, and from 2002 to 2003 was a research engineer in the Autonomous Systems Group at the Charles Stark Draper Laboratory. His current research interests focus on model predictive control, robust optimization and control of fluid flows.