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Stabilizing a System With an Unbounded Random Gain Using Only Finitely Many Bits

Kostina, Victoria and Peres, Yuval and Ranade, Gireeja and Sellke, Mark (2021) Stabilizing a System With an Unbounded Random Gain Using Only Finitely Many Bits. IEEE Transactions on Information Theory, 67 (4). pp. 2554-2561. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:20210205-093044649

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Abstract

We study the stabilization of a linear control system with an unbounded random system gain where the controller must act based on a rate-limited observation of the state. More precisely, we consider the system X_(n+1)=A_nX_n+W_n−U_n, where the A_n’s are drawn independently at random at each time n from a known distribution with unbounded support, and where the controller receives at most R bits about the system state at each time from an encoder. We provide a time-varying achievable strategy to stabilize the system in a second-moment sense with fixed, finite R. While our previous result provided a strategy to stabilize this system using a variable-rate code, this work provides an achievable strategy using a fixed-rate code. The strategy we employ to achieve this is time-varying and takes different actions depending on the value of the state. It proceeds in two modes: a normal mode (or zoom-in), where the realization of A_n is typical, and an emergency mode (or zoom-out), where the realization of A_n is exceptionally large. To analyze the performance of the scheme we construct an auxiliary sequence that bounds the state X_n, and then bound auxiliary sequence in both the zoom-in and zoom-out modes.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/tit.2021.3053140DOIArticle
https://arxiv.org/abs/1805.05535arXivDiscussion Paper
https://resolver.caltech.edu/CaltechAUTHORS:20181126-144509160Related ItemConference Paper
ORCID:
AuthorORCID
Kostina, Victoria0000-0002-2406-7440
Peres, Yuval0000-0001-5456-6323
Ranade, Gireeja0000-0002-6747-4492
Sellke, Mark0000-0001-9166-8185
Additional Information:© 2021 IEEE. Manuscript received August 6, 2019; revised July 20, 2020; accepted December 7, 2020. Date of publication February 1, 2021; date of current version March 18, 2021. The work of Victoria Kostina was supported in part by the National Science Foundation (NSF) under Grant CCF-1751356 and in part by the Simons Institute for the Theory of Computing. The work of Yuval Peres was supported in part by NSF under Grant DMS-1900008. The work of Gireeja Ranade was supported by the Simons Institute for the Theory of Computing. This article was presented in part at the 2018 IEEE International Symposium on Information Theory. The authors would like to thank Miklós Rácz and Serdar Yüksel for interesting discussions regarding this problem. They are very grateful to the reviewers whose feedback has greatly improved the presentation of this work, as well as to the reviewers of the ISIT paper. They would also like to thank Microsoft Research, where part of the work was performed.
Funders:
Funding AgencyGrant Number
NSFCCF-1751356
Simons Institute for the Theory of ComputingUNSPECIFIED
NSFDMS-1900008
Microsoft ResearchUNSPECIFIED
Subject Keywords:Control systems, communication channels, parameter uncertainty, informational bottlenecks
Issue or Number:4
Record Number:CaltechAUTHORS:20210205-093044649
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210205-093044649
Official Citation:V. Kostina, Y. Peres, G. Ranade and M. Sellke, "Stabilizing a System With an Unbounded Random Gain Using Only Finitely Many Bits," in IEEE Transactions on Information Theory, vol. 67, no. 4, pp. 2554-2561, April 2021, doi: 10.1109/TIT.2021.3053140
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107926
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:05 Feb 2021 23:19
Last Modified:26 Mar 2021 14:17

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