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Control over Gaussian Channels With and Without Source-Channel Separation

Khina, Anatoly and Riedel Gårding, Elias and Pettersson, Gustav M. and Kostina, Victoria and Hassibi, Babak (2019) Control over Gaussian Channels With and Without Source-Channel Separation. IEEE Transactions on Automatic Control, 64 (9). pp. 3690-3705. ISSN 0018-9286. https://resolver.caltech.edu/CaltechAUTHORS:20190425-110709737

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Abstract

We consider the problem of controlling an unstable linear plant with Gaussian disturbances over an additive white Gaussian noise channel with an average transmit power constraint, where the signaling rate of communication may be different from the sampling rate of the underlying plant. Such a situation is quite common since sampling is done at a rate that captures the dynamics of the plant and that is often lower than the signaling rate of the communication channel. This rate mismatch offers the opportunity of improving the system performance by using coding over multiple channel uses to convey a single control action. In a traditional, separation-based approach to source and channel coding, the analog message is first quantized down to a few bits and then mapped to a channel codeword whose length is commensurate with the number of channel uses per sampled message. Applying the separation-based approach to control meets its challenges: first, the quantizer needs to be capable of zooming in and out to be able to track unbounded system disturbances, and second, the channel code must be capable of improving its estimates of the past transmissions exponentially with time, a characteristic known as anytime reliability. We implement a separated scheme by leveraging recently developed techniques for control over quantized-feedback channels and for efficient decoding of anytime-reliable codes. We further propose an alternative, namely, to perform analog joint source–channel coding, by this avoiding the digital domain altogether. For the case where the communication signaling rate is twice the sampling rate, we employ analog linear repetition as well as Shannon–Kotel’nikov maps to show a significant improvement in stability margins and linear-quadratic costs over separation-based schemes. We conclude that such analog coding performs better than separation, and can stabilize all moments as well as guarantee almost-sure stability.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TAC.2019.2912255DOIArticle
ORCID:
AuthorORCID
Khina, Anatoly0000-0003-2359-1678
Riedel Gårding, Elias0000-0003-4143-9207
Pettersson, Gustav M.0000-0002-4793-5212
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2019 IEEE. Manuscript received August 11, 2018; accepted November 3, 2018. Date of publication April 19, 2019; date of current version August 28, 2019. This work was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant 708932. The work of E. Riedel Gårding was supported by the National Science Foundation (NSF) under Grant CCF-1566567 through the SURF program. The work of G. M. Pettersson was supported by The Boeing Company under the SURF program. The work of V. Kostina was supported in part by the NSF under Grant CCF-1566567. The work of B. Hassibi was supported in part by the NSF under Grant CNS-0932428, Grant CCF-1018927, Grant CCF-1423663, and Grant CCF-1409204, by a grant from Qualcomm Inc., by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund, and by King Abdullah University of Science and Technology. This paper was presented in part at the IEEE Conference on Decision and Control, Las Vegas, NV, USA, Dec. 2016. This work was done in part while A. Khina and V. Kostina were visiting the Simons Institute for the Theory of Computing. Recommended by Associate Editor K. Kashima. The authors thank H. Yıldız for valuable discussions and help with parts of the simulation.
Funders:
Funding AgencyGrant Number
Marie Curie Fellowship708932
NSFCCF-1566567
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Boeing CompanyUNSPECIFIED
NSFCNS-0932428
NSFCCF-1018927
NSFCCF-1423663
NSFCCF-1409204
Qualcomm Inc.UNSPECIFIED
JPL President and Director's FundUNSPECIFIED
King Abdullah University of Science and Technology (KAUST)UNSPECIFIED
Subject Keywords:Networked control systems, Gaussian channel, combined source–channel coding, quantization, Lloyd–Max algorithm, channel coding, tree codes
Issue or Number:9
Record Number:CaltechAUTHORS:20190425-110709737
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190425-110709737
Official Citation:A. Khina, E. R. Gårding, G. M. Pettersson, V. Kostina and B. Hassibi, "Control Over Gaussian Channels With and Without Source–Channel Separation," in IEEE Transactions on Automatic Control, vol. 64, no. 9, pp. 3690-3705, Sept. 2019. doi: 10.1109/TAC.2019.2912255
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94970
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Apr 2019 19:56
Last Modified:03 Oct 2019 21:09

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