Elements of a Nonstochastic Theory of Information

Girish Nair

Department of Electrical and Electronic Engineering at the University of Melbourne

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, Markovness and information, without assuming a probability space. This talk describes a framework for doing so, leading to the construction of a “maximin” information functional for nonstochastic variables. In this framework, the largest maximin information rate through a memoryless, error-prone channel coincides exactly with its zero-error capacity without feedback. The concept of directed maximin information is then introduced and shown to characterise the zero-error feedback capacity in a similar way. Time permitting, connections to the problems of estimating and stabilising the states of linear systems via noisy channels are discussed.

Biography:

Dr. Girish N. Nair was born in Malaysia and obtained a B. Engineering (Elec., 1st class Hons.) in 1994, B.Science (math.) in 1995, and Ph.D. (elec. eng.) in 2000, 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. His research interests lie in information theory and networked control, and his work was awarded a SIAM Outstanding Paper Prize in 2006, and the Best Theory Paper Prize at the UKACC Int. Conf. Control, Cambridge Uni., 2000. He was an associate editor for the SIAM Jour. Control and Optimization from 2006 - 2011, and is currently an associate editor for the IEEE Trans. Automatic Control. He has held visiting positions at the University of Padova and Boston University, and is presently visiting ETH Zurich till Jan. 2014.