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Rate of prefix-free codes in LQG control systems
KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0001-9940-5929
KTH, School of Electrical Engineering (EES), Communication Theory.ORCID iD: 0000-0002-0036-9049
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0003-1835-2963
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2016 (English)In: 2016 IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers (IEEE), 2016, Vol. 2016, 2399-2403 p., 7541729Conference paper (Refereed)
Abstract [en]

In this paper, we consider a discrete time linear quadratic Gaussian (LQG) control problem in which state information of the plant is encoded in a variable-length binary codeword at every time step, and a control input is determined based on the codewords generated in the past. We derive a lower bound of the rate achievable by the class of prefix-free codes attaining the required LQG control performance. This lower bound coincides with the infimum of a certain directed information expression, and is computable by semidefinite programming (SDP). Based on a technique by Silva et al., we also provide an upper bound of the best achievable rate by constructing a controller equipped with a uniform quantizer with subtractive dither and Shannon-Fano coding. The gap between the obtained lower and upper bounds is less than 0:754r + 1 bits per time step regardless of the required LQG control performance, where r is the rank of a signal-to-noise ratio matrix obtained by SDP, which is no greater than the dimension of the state.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2016. Vol. 2016, 2399-2403 p., 7541729
Series
IEEE International Symposium on Information Theory, ISSN 2157-8095
Keyword [en]
Codes (symbols), Information theory, Matrix algebra, Directed information, Linear quadratic Gaussian control, Lower and upper bounds, Semi-definite programming, Shannon-Fano coding, State information, Subtractive dither, Uniform quantizer, Signal to noise ratio
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-194964DOI: 10.1109/ISIT.2016.7541729ISI: 000390098702093ScopusID: 2-s2.0-84985987098ISBN: 9781509018062 (print)OAI: oai:DiVA.org:kth-194964DiVA: diva2:1048853
Conference
2016 IEEE International Symposium on Information Theory, ISIT 2016, Universitat Pompeu Fabra Barcelona, Spain, 10 July 2016 through 15 July 2016
Note

QC 20161122

Available from: 2016-11-22 Created: 2016-11-01 Last updated: 2017-01-31Bibliographically approved

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