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

Victoria Kostina, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations


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.
Original languageEnglish (US)
Title of host publication2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Number of pages8
ISBN (Print)9781538665961
StatePublished - 2018
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-24
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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