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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: IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers (IEEE), 2016, 2399-2403 p.Conference 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. 2399-2403 p.
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.2016.7541729ScopusID: 2-s2.0-84985987098ISBN: 9781509018062OAI: oai:DiVA.org:kth-194964DiVA: diva2:1048853
Conference
2016 IEEE International Symposium on Information Theory, ISIT 2016, 10 July 2016 through 15 July 2016
Note

QC 20161122

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

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Tanaka, TakashiJohansson, Karl H.Oechtering, T. J.Sandberg, HenrikSkoglund, Mikael
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