Stabilizing a System with an Unbounded Random Gain Using Only Finitely Many 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_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.
Additional Information
© 2018 IEEE. We thank Miklós Rácz and Serdar Yüksel for interesting discussions regarding this problem.Attached Files
Submitted - 1805.05535.pdf
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Additional details
- Eprint ID
- 91189
- Resolver ID
- CaltechAUTHORS:20181126-144509160
- Created
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2018-11-26Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field