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. https://resolver.caltech.edu/CaltechAUTHORS:20181126-144509160
![]() |
PDF
- Submitted Version
See Usage Policy. 331Kb |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20181126-144509160
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: |
| |||||||||
ORCID: |
| |||||||||
Additional Information: | © 2018 IEEE. We thank Miklós Rácz and Serdar Yüksel for interesting discussions regarding this problem. | |||||||||
Record Number: | CaltechAUTHORS:20181126-144509160 | |||||||||
Persistent URL: | https://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: | 03 Oct 2019 20:32 |
Repository Staff Only: item control page