Seminar Details
2013-11-12 (14.00) : Elements of a Nonstochastic Information Theory
At Euler building
Organized by Mathematical Engineering
Speaker :
Girish Nair (University of Melbourne, Australia)
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 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.