NDLI: Fundamental limitations of performance in the presence of finite capacity feedback

Content Provider	IEEE Xplore Digital Library
Author	Martins, N.C. Dahleh, M.A.
Copyright Year	2005
Description	Author affiliation: Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA (Martins, N.C.; Dahleh, M.A.)
Abstract	This paper addresses a fundamental limitation of performance for feedback systems, in the presence of a communication channel. The feedback loop comprises a discrete-time, linear and time-invariant plant, a channel, an encoder and a decoder which may also embody a controller. Measurements of the plant's output must be encoded for transmission over the channel. Information, at the other end of the channel, is decoded and used to generate a control signal, which is additively disturbed by a Gaussian and stationary stochastic process. We derive an inequality of the form L/spl I.bar/ /spl ges/ /spl Sigma/ max{0, log(\|/spl lambda//sub i/(A)\|)} - C/sub channel/, where L/spl I.bar/ is a measure of disturbance rejection, A is the open loop dynamic matrix and C/sub channel/ is the Shannon capacity of the channel. Our measure L/spl I.bar/ is non-positive and smaller L/spl I.bar/ indicates better rejection (attenuation), while L/spl I.bar/ = 0 signifies no rejection. Previous results show that C/sub channel/ > /spl Sigma/max{0, log(\|/spl lambda//sub i/(A)\|)} is a necessary condition for stability and now we show that the extra rate C/sub channel/ - /spl Sigma/max{0, log(\|/spl lambda//sub i/(A)\|)} determines a fundamental limitation for disturbance rejection. Additionally, we prove that, under stationarity assumptions, L/spl I.bar/ admits a log-sensitivity integral representation. We contrast our condition with Rode's integral formula and the water-bed effect. The new inequality shows explicitly how the capacity of the channel limits closed loop performance.
Sponsorship	American Automatic Control Council
Starting Page	79
Ending Page	86
File Size	381986
Page Count	8
File Format	PDF
ISBN	0780390989
ISSN	07431619
e-ISBN	0780390997
DOI	10.1109/ACC.2005.1469912
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-06-08
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Decoding Channel capacity Communication channels Feedback loop Linear feedback control systems Communication system control Signal generators Open loop systems Signal processing Stochastic processes
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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