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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 (2018) Stabilizing a System with an Unbounded Random Gain Using Only Finitely Many Bits. In: 2018 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 2256-2260. ISBN 978-1-5386-4780-6. http://resolver.caltech.edu/CaltechAUTHORS:20181126-144509160

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Abstract

We study the stabilization of an unpredictable linear control system where the controller must act based on a rate-limited observation of the state. More precisely, we consider the system X_(n+1) = A_n X_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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT.2018.8437548DOIArticle
https://arxiv.org/abs/1805.05535arXivDiscussion Paper
ORCID:
AuthorORCID
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2018 IEEE. We thank Miklós Rácz and Serdar Yüksel for interesting discussions regarding this problem.
Record Number:CaltechAUTHORS:20181126-144509160
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181126-144509160
Official Citation:V. Kostina, Y. Peres, G. Ranade and M. Sellke, "Stabilizing a System with an Unbounded Random Gain Using Only Finitely Many Bits," 2018 IEEE International Symposium on Information Theory (ISIT), Vail, CO, 2018, pp. 2256-2260. doi: 10.1109/ISIT.2018.8437548
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91189
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Nov 2018 23:08
Last Modified:17 Jun 2019 16:49

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