A journey through data-rate theorems for communication and control By Massimo Franceschetti
In this talk, we address the problem of mean-square stabilization of a discrete-time linear dynamical system where the estimated state is transmitted for control over a digital communication channel. This arises in several emerging applications including remote robot control, automated highway navigation using wireless sensor systems, and automatic control for pursuit evasion games.
In this context, a data-rate theorem refers to the minimum information rate required to guarantee the stability of the system over a given communication channel. Loosely speaking, it states that the information rate to be supported by the channel must be large enough compared to the unstable modes of the system, so that it can compensate for the expansion of the state during the communication process.
Since its first rigorous formulation about a decade ago, and driven by technological advancements of embedded systems for control, there has been a growing interest in stating a data rate theorem for the most general communication model.
We will review a series of contributions by different groups (including ours), sketching mathematical arguments based on a blend of information-theoretic and control-theoretic tools. We will also try to draw a connection between results in control and some recent advancements in feedback communication and will conclude mentioning some open problems in the field.
Bio: Massimo Franceschetti is associate professor in the Department of Electrical and Computer Engineering of University of California at San Diego. He received the Laurea degree, magna cum laude, in Computer Engineering from the University of Naples in 1997, and the M.S. and Ph.D. degrees in Electrical Engineering from the California Institute of Technology in 1999, and 2003. Before joining UCSD, he was a post-doctoral scholar at University of California at Berkeley for two years. Prof. Franceschetti was awarded the C. H. Wilts Prize in 2003 for best doctoral thesis in Electrical Engineering at Caltech; the S. A. Schelkunoff award in 2005 for best paper in the IEEE Transactions on Antennas and Propagation; an NSF CAREER award in 2006, an ONR Young Investigator award in 2007; and the IEEE Communications society best tutorial paper award in 2010. He has held visiting positions at at the Vrije Universiteit Amsterdam in the Netherlands, the Ecole Polytechnique Federale de Lausanne in Switzerland, and the University of Trento in Italy. He is associate editor for communication networks of the IEEE Transactions on Information Theory and has served as guest editor for two issues of the IEEE Journal on Selected Areas in Communication. His research interests are in communication systems theory and include random networks, wave propagation in random media, wireless communication, and control over networks.