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Rate-cost tradeoffs in scalar LQG control and tracking with side information

Kostina, Victoria and Hassibi, Babak (2018) Rate-cost tradeoffs in scalar LQG control and tracking with side information. In: 56th Annual Allerton Conference on Communication, Control, and Computing. IEEE , Piscataway, NJ, pp. 421-428. ISBN 978-1-5386-6596-1. http://resolver.caltech.edu/CaltechAUTHORS:20190329-091228468

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Abstract

Consider a control problem in which a remote controller chooses its control action based on two kinds of information about the system state: the information it receives from the system via a rate-constrained feedback link, and side information - a noisy measurement of the system state it observes directly. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate, the expected cost b and the quality of side information. Due to a separation principle between estimation and control, we focus on the tracking problem, where the goal is to track the system state rather than to control it. We introduce the causal rate-distortion function with side information at the decoder. It is expressed in terms of directed mutual information, and it extends the classical (noncausal) Wyner-Ziv rate-distortion function to real-time tracking problems with causality constraints and memory of the past at both encoder and decoder. We compute that function in the scalar linear Gaussian setting; we draw a link with the Kalman filter; we show that making side information available also at the encoder does not help to improve the optimal tradeoffs.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ALLERTON.2018.8635889DOIArticle
ORCID:
AuthorORCID
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2018 IEEE. The work of Victoria Kostina was supported in part by the National Science Foundation (NSF) under grant CCF-1751356. The work of Babak 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, and by King Abdullah University of Science and Technology.
Funders:
Funding AgencyGrant Number
NSFCCF-1751356
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:Linear stochastic control, LQG control, remote control, rate-distortion tradeoff, causal rate-distortion theory, Gauss-Markov source, real-time tracking, Wyner-Ziv rate-distortion function
Record Number:CaltechAUTHORS:20190329-091228468
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190329-091228468
Official Citation:V. Kostina and B. Hassibi, "Rate-cost tradeoffs in scalar LQG control and tracking with side information," 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA, 2018, pp. 421-428. doi: 10.1109/ALLERTON.2018.8635889
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94290
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:29 Mar 2019 16:30
Last Modified:29 Mar 2019 16:30

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