Elements of a nonstochastic information theory

Abstract:

In communications, unknown quantities are usually modelled as random variables. In contrast,control theory often treats uncertainties as bounded unknowns having no statistical structure. The area of networked control combines both fields and raises the question of whether it is possible to construct meaningful analogues of stochastic concepts such as independence, Markovianness and information, without assuming a probability space. This talk introduces a framework for doing so, leading in particular to the construction of a ”maximin” information functional for non-stochastic variables. It is shown that, in this framework, the largest maximin information rate through a memoryless, error-prone channel coincides exactly with its block-coding zero-error capacity without feedback. This leads to a tight condition for the achievability of exponential uniform convergence when estimating the state of an unperturbed linear system over such a channel. Time permitting, recent results relating the concept of ”directed” maximin information to zero-error feedback capacity and feedback control will also be discussed.

Presentation Slildes

Biography:Girish Nair was born in Malaysia, and obtained a B.E. (Elec., 1st class hons.), B.Sc. (math.) and Ph.D. (elec. eng.)  on scholarships from the Australian government and the University of Melbourne. He is currently an associate professor in the Department of Electrical and Electronic Engineering at the University of Melbourne, and has held visiting positions at the University of Padova and Boston University. He was an associate editor for the SIAM Journal on Control and Optimization from 2006-11, and is currently an associate editor for the IEEE Transactions on Automatic Control. His research interests lie in information theoretic control and he has received several prizes, including a SIAM Outstanding Paper Prize 2003-5 
and the Best Theory Paper Prize at the UKACC Int. Conf. Control, Cambridge Uni., 2000.