A Convex Approach to Control of Delayed and PDE Systems with Application to Magnetic Confinement of Plasma in Fusion Reactors
Jan 31, 2014
from 10:30 AM to 12:00 PM
|Where||Engr. IV Bldg., Maxwell Room 57-124|
|Contact Name||Prof. Panagiotis Christofides|
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Matthew M. Peet
Arizona State University
In this talk, we explore the possibilities and limits of using computation to analyze and control complex distributed systems such as those which govern the magneto-hydrodynamics of a Tokamak. We begin the talk by showing how convex optimization and Sum-of-Squares can be used to optimize over the cone of positive polynomials. This result allows us to use positive matrices to parameterize positive Lyapunov functions for nonlinear differential equations. We then extend these results by showing how positive matrices can be used to parameterize the measures of energy which arise in infinite-dimensional systems such as those governed by delay-differential equations or PDEs. We then study the implications of this result for stability and control of systems with delay. Next, we discuss the problem of MHD stability in plasma and present several PDE models. We then show how we can use our results to analyze and design real-time controllers for these models which use only point observations and sources of non-inductive current.
Matthew M. Peet received B.S. degrees in Physics and in Aerospace Engineering from the University of Texas at Austin in 1999 and the M.S. and Ph.D. in Aeronautics and Astronautics from Stanford University in 2001 and 2006, respectively. He was a Postdoctoral Fellow at the National Institute for Research in Computer Science and Control (INRIA) near Paris, France, from 2006-2008. From 2008-2012 he was an Assistant Professor of Aerospace Engineering in the Mechanical, Materials, and Aerospace Engineering Department of the Illinois Institute of Technology. He is currently an Assistant Professor of Aerospace Engineering at Arizona State University (ASU) in the School for Engineering of Matter, Transport and Energy and director of the Cybernetic Systems and Controls Laboratory. A recent NSF CAREER awardee, his current research interests are in the role of computation as it is applied to the understanding and control of complex and large-scale systems.