In this talk, we explore the possibilities and limits of using computation to analyze and control complex systems. The systems we consider are modeled by nonlinear, delayed or partial-differential equations. We begin the talk by proving that stability of a nonlinear vector field is decidable and deriving a bound on the complexity as a function of the rate of decay. This derivation explores concepts from convex optimization and converse Lyapunov theory. We then discuss extending these results to the difficult problems of stability and control of systems with delay or spatial dimension. Finally, we show how these computational techniques can be applied to knowledge discovery in immunology.
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 where he worked in the SISYPHE and BANG groups. From 2008-2012 he was an Assistant Professor 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. He has studied the use of optimization algorithms and Sum-of-Squares programming for the analysis of nonlinear systems and partial differential equations and has worked with applications in information networks and cancer therapy.