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Algorithms for Optimal Control with Fixed-Rate Feedback

Khina, Anatoly and Nakahira, Yorie and Su, Yu-Su and Hassibi, Babak (2017) Algorithms for Optimal Control with Fixed-Rate Feedback. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 6015-6020. ISBN 978-1-5090-2874-0. https://resolver.caltech.edu/CaltechAUTHORS:20180126-083658723

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Abstract

We consider a discrete-time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimize performance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/CDC.2017.8264569DOIArticle
http://ieeexplore.ieee.org/document/8264569/PublisherArticle
ORCID:
AuthorORCID
Khina, Anatoly0000-0003-2359-1678
Additional Information:© 2017 IEEE. Date Added to IEEE Xplore: 23 January 2018. The work of A. Khina has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 708932. The work of Y. Nakahira was funded by grants from AFOSR and NSF, and gifts from Cisco, Huawei, and Google. The work of Y. Su was supported in part by NSF through AitF-1637598. The work of B. Hassibi was supported in part by the NSF under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund, by King Abdulaziz University, and by King Abdullah University of Science and Technology. The authors thank V. Kostina for valuable discussions.
Funders:
Funding AgencyGrant Number
Marie Skłodowska-Curie708932
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
CiscoUNSPECIFIED
HuaweiUNSPECIFIED
GoogleUNSPECIFIED
NSFAitF-1637598
NSFCNS-0932428
NSFCCF-1018927
NSFCCF-1423663
NSFCCF-1409204
Qualcomm Inc.UNSPECIFIED
NASA/JPL President and Director's FundUNSPECIFIED
King Abdulaziz UniversityUNSPECIFIED
King Abdullah University of Science and Technology (KAUST)UNSPECIFIED
Record Number:CaltechAUTHORS:20180126-083658723
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180126-083658723
Official Citation:A. Khina, Y. Nakahira, Y. Su and B. Hassibi, "Algorithms for optimal control with fixed-rate feedback," 2017 IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, Australia, 2017, pp. 6015-6020. doi: 10.1109/CDC.2017.8264569
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84538
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:31 Jan 2018 00:38
Last Modified:03 Oct 2019 19:19

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