The value of information in event triggering: can we beat the data-rate theorem?

Abstract: In networked control, data-rate theorems relate the amount of information that the feedback channel between estimator and controller must be able to supply to guarantee stability, to the amount of informationrequested by the plant. They represent a cornerstone of the theory of cyber-physical systems (CPS) and have been studied for more than a decade. On the other hand, the need to use distributed resources efficiently in CPS has led to event-triggering control techniques based on the idea of sending information in an opportunistic manner between the controller and the plant. After reviewing the basics of the data rate theorems, we illustrate how these are to be modified in the presence of an event-triggered implementation. The main observation is that the act of triggeringreveals information about the system’s state and  can be exploited for stabilization, thus effectively invalidating “classic” formulations of the theorem. An extended formulation reveals a phase transition behavior of the transmission rate required for stabilization as a function of the communication delay. It is shown that for low values of the delay the timing information carried by the triggering events is large and the system can be stabilized with any positive rate. On the other hand, when the delay exceeds a certain threshold that depends on the given triggeringstrategy, the timing information alone is not enough to achieve stabilization and the rate must begin to grow, eventually becoming larger than what required by the classic data-rate theorem. The critical point where the transmission rate equals the one imposed by the data-rate theorem occurs when the delay equals the inverse of the entropy rate of the plant, representing the intrinsic rate at which the system generates information. At this critical point, the timing information supplied by event triggering is completely balanced by the information loss due to the communication delay.

Bio: Massimo Franceschetti received the Laurea degree (with highest honors) in computer engineering from the University of Naples, Naples, Italy, in 1997, the M.S. and Ph.D. degrees in electrical engineering from the California Institute of Technology, Pasadena, CA, in 1999, and 2003, respectively. He is Professor of Electrical and Computer Engineering at the University of California at San Diego (UCSD). Before joining UCSD, he was a postdoctoral scholar at the University of California at Berkeley for two years. He has held visiting positions at the Vrije Universiteit Amsterdam, the Ecole Polytechnique Federale de Lausanne, and the University of Trento. His research interests are in physical and information-based foundations of communication and control systems. He is co-author of the book “Random Networks for Communication” published by Cambridge University Press. Dr. Franceschetti served as Associate Editor for the IEEE Transactions on Information Theory (2009-2012) and for the IEEE Transactions on Control of Network Systems (2013-16) and as Guest Associate Editor of the IEEE Journal on Selected Areas in Communications (2008, 2009). He is currently serving as Associate Editor of the IEEE Transactions on Network Science and Engineering. He 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, a National Science Foundation (NSF) CAREER award in 2006, an Office of Naval Research (ONR) Young Investigator Award in 2007, the IEEE Communications Society Best Tutorial Paper Award in 2010, and the IEEE Control theory society Ruberti young researcher award in 2012.

Hosted by: Paul Bogdan