Rate-cost tradeoffs in control

Victoria Kostina; Babak Hassibi

doi:10.1109/allerton.2016.7852366

Rate-cost tradeoffs in control

Victoria Kostina, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

16 Scopus citations

Abstract

Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state.

Original language	English (US)
Title of host publication	2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	1157-1164
Number of pages	8
ISBN (Print)	9781509045501
DOIs	https://doi.org/10.1109/allerton.2016.7852366
State	Published - Feb 13 2017
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors acknowledge many stimulating discussions with Dr. Anatoly Khina and his helpful comments on the earlier versions of the manuscript. The authors are also grateful to Ayush Pandey, who with incessant enthusiasm generated the plot in Fig. 2. The work of Victoria Kostina was supported in part by the National Science Foundation (NSF) under Grant CCF-1566567. The work of Babak Hassibi was supported in part by the National Science Foundation 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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10.1109/allerton.2016.7852366

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title = "Rate-cost tradeoffs in control",

abstract = "Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state.",

author = "Victoria Kostina and Babak Hassibi",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: The authors acknowledge many stimulating discussions with Dr. Anatoly Khina and his helpful comments on the earlier versions of the manuscript. The authors are also grateful to Ayush Pandey, who with incessant enthusiasm generated the plot in Fig. 2. The work of Victoria Kostina was supported in part by the National Science Foundation (NSF) under Grant CCF-1566567. The work of Babak Hassibi was supported in part by the National Science Foundation 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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doi = "10.1109/allerton.2016.7852366",

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N2 - Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state.

AB - Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state.

UR - http://hdl.handle.net/10754/623584

UR - http://ieeexplore.ieee.org/document/7852366/

UR - http://www.scopus.com/inward/record.url?scp=85010796961&partnerID=8YFLogxK

U2 - 10.1109/allerton.2016.7852366

DO - 10.1109/allerton.2016.7852366

M3 - Conference contribution

SN - 9781509045501

SP - 1157

EP - 1164

BT - 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -

Rate-cost tradeoffs in control

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