The information cost of loop shaping over gaussian channels

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

4 Scopus citations

Abstract

In this paper, we extend the results of our previous work on feedback stabilization and feedback communication to include the presence of an external input acting as a output disturbance on the feedback system. Rather than on the communication system, we focus on the control system. We show that the Directed Information still characterizes the information rate flowing through the channel, and that it is constant for a given open loop Degree of Instability and the channel model. This indicates that, in our case, loop shaping does not affect the rate through the channel but only the transmission power if the degree of instability is kept constant. For the memoryless AWGN channel we characterize the required transmission power in a closed form which relates a function of the required transmission power to the sum two rates: one given by the Directed Information, the other lost due to the non flat frequency shaping of the Sensitivity and expressed in term of a relative entropy. This result provides a new interpretation to the H∞ Sensitivity minimization problem which is based on information theoretic concepts.

Original languageEnglish (US)
Title of host publicationProceedings of the 20th IEEE International Symposium on Intelligent Control, ISIC '05 and the 13th Mediterranean Conference on Control and Automation, MED '05
PublisherIEEE Computer Society
Pages1097-1102
Number of pages6
ISBN (Print)0780389360, 9780780389366
DOIs
StatePublished - 2005
Externally publishedYes
Event20th IEEE International Symposium on Intelligent Control, ISIC '05 and the13th Mediterranean Conference on Control and Automation, MED '05 - Limassol, Cyprus
Duration: Jun 27 2005Jun 29 2005

Publication series

NameProceedings of the 20th IEEE International Symposium on Intelligent Control, ISIC '05 and the 13th Mediterranean Conference on Control and Automation, MED '05
Volume2005

Other

Other20th IEEE International Symposium on Intelligent Control, ISIC '05 and the13th Mediterranean Conference on Control and Automation, MED '05
CountryCyprus
CityLimassol
Period6/27/056/29/05

Keywords

  • Feedback capacity
  • Fundamental limits on communication and control
  • Networked Systems

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