Handle URI:
http://hdl.handle.net/10754/623584
Title:
Rate-cost tradeoffs in control
Authors:
Kostina, Victoria; Hassibi, Babak
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.
Citation:
Kostina V, Hassibi B (2016) Rate-cost tradeoffs in control. 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton). Available: http://dx.doi.org/10.1109/allerton.2016.7852366.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Conference/Event name:
54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
Issue Date:
13-Feb-2017
DOI:
10.1109/allerton.2016.7852366
Type:
Conference Paper
Sponsors:
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorKostina, Victoriaen
dc.contributor.authorHassibi, Babaken
dc.date.accessioned2017-05-15T10:35:09Z-
dc.date.available2017-05-15T10:35:09Z-
dc.date.issued2017-02-13en
dc.identifier.citationKostina V, Hassibi B (2016) Rate-cost tradeoffs in control. 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton). Available: http://dx.doi.org/10.1109/allerton.2016.7852366.en
dc.identifier.doi10.1109/allerton.2016.7852366en
dc.identifier.urihttp://hdl.handle.net/10754/623584-
dc.description.abstractConsider 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.en
dc.description.sponsorshipThe 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.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.subjectShannon's lower bounden
dc.subjectLinear stochastic controlen
dc.subjectrate-distortion tradeoffen
dc.subjecthigh resolutionen
dc.subjectsequential rate-distortion theoryen
dc.titleRate-cost tradeoffs in controlen
dc.typeConference Paperen
dc.identifier.journal2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)en
dc.conference.date2016-09-27 to 2016-09-30en
dc.conference.name54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016en
dc.conference.locationMonticello, IL, USAen
dc.contributor.institutionCalifornia Institute of Technology, United Statesen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.