Rate of prefix-free codes in LQG control systems
2016 (English)In: IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers (IEEE), 2016, 2399-2403 p.Conference paper (Refereed)
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.
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
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-194964DOI: 10.1109/ISIT.2016.7541729ScopusID: 2-s2.0-84985987098ISBN: 9781509018062OAI: oai:DiVA.org:kth-194964DiVA: diva2:1048853
2016 IEEE International Symposium on Information Theory, ISIT 2016, 10 July 2016 through 15 July 2016
QC 201611222016-11-222016-11-012016-11-22Bibliographically approved