Title: The Meaning of Structure in Distributed Dynamical Systems
Speaker: Sean Warnick, Associate Professor of Computer Science, Brigham Young University
Abstract: Large, complex, network systems are characterized by both their dynamic behavior as well as their inherent structure. But what exactly does “structure” mean? Mathematicians use graphs to describe structural relationships in a variety of settings. Engineers look to the arrangement of components to describe how a system is interconnected. Scientists measure variables and note the interaction structure as one variable impacts another. Are all of these notions of structure consistent, or do they have nuances that distinguish one notion of structure from another?
In this talk we explore these ideas using linear time-invariant (LTI) systems as familiar ground to make the concepts precise. In so doing, we introduce Dynamical Structure Functions as a partial-structure representation of LTI systems and show how this representation differs from the system’s state representation or its transfer function. We then show how dynamical structure functions can be a useful tool for addressing the network reconstruction of biochemical reaction networks, detecting intrusion anomalies in wireless mesh networks, characterizing the vulnerability of a linear system, or synthesizing stabilizing distributed controllers.
Speaker Bio: Sean Warnick is an Associate Professor of Computer Science at Brigham Young University, where he leads the Information and Decision Algorithms Laboratories. He earned his Ph.D. and MS from MIT in 2003 and 1996, respectively, and he was named the Outstanding Graduate of the College of Engineering and Applied Sciences in 1993 by Arizona State University. He has been a visiting professor at Cambridge University (summer 2006) and the University of Maryland (summer 2008), and he was named “The Distinguished Visiting Professor” by the National Security Agency in 2008, 2009, and 2010 for his work with the NSA’s Operations Research, Modelling and Simulation Group. Besides thinking about the meaning of structure and the associated problems of mathematically representing complex systems, he has worked on identification and control (e.g. of grating-stabilized external cavity diode lasers), robustness analysis (e.g. of coalitions in gradient differential games in the market power analyses of industrial organization networks), and model-reduction (e.g. for flexible batch manufacturing systems in the max-plus algebra). His current interests continue to include model-reduction (e.g. via parameter space compression), robustness analysis (e.g. as a theory of cyber-security), and identification and control (e.g. of crop systems, financial markets, and social media).