Convergence of fundamental limitations in information, estimation, and control

Jialing Liu, Nicola Elia

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

The emerging study of integrating information theory and control systems theory has attracted considerable attention by researchers, mainly motivated by problems involving communication channels in loops. The main goals of the present paper are to introduce a new perspective to this study, namely the perspective of integrating information, estimation, and control, and to unify fundamental limitations in information, estimation, and control. In particular, we establish, over a discrete-time Gaussian channel with memory, a general equivalence among feedback communication, estimation, and feedback stabilization. We then show that, the achievable information rate in the feedback communication problem can be alternatively given by the decay rate of the Cramer-Rao bound (CRB) in the associated estimation problem, or by the Bode sensitivity integral in the associated control problem. Therefore, we conclude that the fundamental limitations in information transmission (i.e. achievable information rate), in information processing (i.e. CRB), and in information utilization (i.e. Bode integral), seemingly different and usually separately treated, are in fact three sides of the same entity. We also briefly discuss the possibility of extending the results to channels in continuous-time and channels not in feedback loops.

Original languageEnglish (US)
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5609-5614
Number of pages6
ISBN (Print)1424401712, 9781424401710
DOIs
StatePublished - Jan 1 2006
Externally publishedYes
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: Dec 13 2006Dec 15 2006

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other45th IEEE Conference on Decision and Control 2006, CDC
CountryUnited States
CitySan Diego, CA
Period12/13/0612/15/06

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