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Stabilizing a system with an unbounded random gain using only a finite number of bits

Kostina, Victoria and Peres, Yuval and Ranade, Gireeja and Sellke, Mark (2018) Stabilizing a system with an unbounded random gain using only a finite number of bits. . (Unpublished)

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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_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.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Kostina, Victoria0000-0002-2406-7440
Additional Information:We thank Miklós Rácz and Serdar Yüksel for interesting discussions regarding this problem. We also thank the ISIT reviewers for their helpful comments.
Record Number:CaltechAUTHORS:20191004-141927403
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99093
Deposited By: Tony Diaz
Deposited On:04 Oct 2019 21:41
Last Modified:04 Oct 2019 21:41

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