The Information cost of sensitivity shaping over Gaussian channels

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

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 an 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 channel model. This indicates that, in our case if the degree of instability is kept constant, loop shaping does not affect the rate through the channel but only the transmission power. 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 due to the non flat frequency shaping of the Sensitivity and expressed in term of a relative entropy. This result provides a new interpretation of the H∞ Sensitivity minimization problem based on Information theory concepts.

Original languageEnglish (US)
Title of host publication43rd Annual Allerton Conference on Communication, Control and Computing 2005
PublisherUniversity of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering
Pages1317-1326
Number of pages10
ISBN (Electronic)9781604234916
StatePublished - Jan 1 2005
Externally publishedYes
Event43rd Annual Allerton Conference on Communication, Control and Computing 2005 - Monticello, United States
Duration: Sep 28 2005Sep 30 2005

Publication series

Name43rd Annual Allerton Conference on Communication, Control and Computing 2005
Volume3

Other

Other43rd Annual Allerton Conference on Communication, Control and Computing 2005
CountryUnited States
CityMonticello
Period9/28/059/30/05

Keywords

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

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