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Rate-cost tradeoffs in control

Kostina, Victoria and Hassibi, Babak (2016) Rate-cost tradeoffs in control. In: 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016. IEEE , Piscataway, NJ, pp. 1157-1164. ISBN 978-1-5090-4551-8. http://resolver.caltech.edu/CaltechAUTHORS:20170221-070702279

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Abstract

Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ALLERTON.2016.7852366DOIArticle
http://ieeexplore.ieee.org/document/7852366/PublisherArticle
https://arxiv.org/abs/1612.02126arXivDiscussion Paper
ORCID:
AuthorORCID
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2016 IEEE. Date of Conference: 27-30 Sept. 2016. Date Added to IEEE Xplore: 13 February 2017. The authors acknowledge many stimulating discussions with Dr. Anatoly Khina and his helpful comments on the earlier versions of the manuscript. The authors are also grateful to Ayush Pandey, who with incessant enthusiasm generated the plot in Fig. 2. The work of Victoria Kostina was supported in part by the National Science Foundation (NSF) under Grant CCF-1566567. The work of Babak Hassibi was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund, and by King Abdullah University of Science and Technology.
Funders:
Funding AgencyGrant Number
NSFCCF-1566567
NSFCNS-0932428
NSFCCF-1018927
NSFCCF-1423663
NSFCCF-1409204
Qualcomm Inc.UNSPECIFIED
JPL President and Director's FundUNSPECIFIED
King Abdullah University of Science and Technology (KAUST)UNSPECIFIED
Subject Keywords:Linear stochastic control, rate-distortion tradeoff, high resolution, sequential rate-distortion theory, Shannon’s lower bound
Record Number:CaltechAUTHORS:20170221-070702279
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170221-070702279
Official Citation:V. Kostina and B. Hassibi, "Rate-cost tradeoffs in control," 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA, 2016, pp. 1157-1164. doi: 10.1109/ALLERTON.2016.7852366
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74415
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:21 Feb 2017 17:36
Last Modified:02 Apr 2019 22:13

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