Stabilizing a system with an unbounded random gain using only a finite number of bits
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_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.
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.Attached Files
Submitted - 1805.05535.pdf
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Additional details
- Eprint ID
- 99093
- Resolver ID
- CaltechAUTHORS:20191004-141927403
- Created
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2019-10-04Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field