[Legacy Report] Seminar: Elements of a Nonstochastic Information Theory

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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 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 to be able to estimating the state of a linear dynamical system over such a channel. Finally, recent results relating the concept of "directed" maximin information to zero-error feedback capacity and feedback control will also be discussed.

Biography
Girish Nair was born in Malaysia, and obtained a B.E.(Elec., 1st class hons.) in 1994, B.Sc.(maths) in 1995 and Ph.D. (elec. eng.) in 2000, on scholarships from the Australian government and Uni. Melbourne. He is currently an Associate Professor in the Department of Electrical and Electronic Engineering at Uni. Melbourne, and has held visiting positions at Uni. Padua, Italy, and Boston Uni., USA. His research interests lie in information-theoretic control and networked systems. He has received several awards, including a SIAM Outstanding Paper Prize for 2003 - 2005, and the UKACC Prize for Best Theory Paper Prize at the International 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.

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