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Stabilizing Dynamical Systems with Fixed-Rate Feedback using Constrained Quantizers

Sabag, Oron and Kostina, Victoria and Hassibi, Babak (2020) Stabilizing Dynamical Systems with Fixed-Rate Feedback using Constrained Quantizers. In: 2020 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 2855-2860. ISBN 9781728164328. https://resolver.caltech.edu/CaltechAUTHORS:20200831-150243516

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Abstract

The stabilization of unstable dynamical systems using rate-limited feedback links is investigated. In the scenario of a constant-rate link and a noise with unbounded support, the fundamental limit of communication is known, but no simple algorithm to achieve it exists. The main challenge in constructing an optimal scheme is to fully exploit the communication resources while occasionally signaling the controller that a special operation needs to be taken due to a large noise observation. In this work, we present a simple and explicit algorithm that stabilizes the dynamical system and achieves the fundamental limits of communication. The new idea is to use a constrained quantizer in which certain patterns of sequences are avoided throughout the quantization process. These patterns are preserved to signal the controller that a zoom-out operation should be initiated due to large noise observation. We show that the constrained quantizer has a negligible effect on the rate, so it achieves the fundamental limit of communication. Specifically, the rate-optimal algorithm is shown to stabilize any β-moment of the state if the noise has a bounded absolute (β +ϵ)-moment for some ϵ > 0 regardless of the other noise characteristics.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/isit44484.2020.9173929DOIArticle
ORCID:
AuthorORCID
Sabag, Oron0000-0002-7907-1463
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2020 IEEE. This work was supported in part by the National Science Foundation (NSF) under grant CCF-1751356. The work of O. Sabag was partially supported by the ISEF postdoctoral fellowship.
Funders:
Funding AgencyGrant Number
NSFCCF-1751356
Israel Scholarship Education FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20200831-150243516
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200831-150243516
Official Citation:O. Sabag, V. Kostina and B. Hassibi, "Stabilizing Dynamical Systems with Fixed-Rate Feedback using Constrained Quantizers," 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 2020, pp. 2855-2860, doi: 10.1109/ISIT44484.2020.9173929
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105182
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Sep 2020 00:00
Last Modified:09 Sep 2020 00:00

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