Algorithms for optimal control with fixed-rate feedback

Anatoly Khina, Yorie Nakahira, Yu Su, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

18 Scopus citations


We consider a discrete-Time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimize performance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions.

Original languageEnglish
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781509028733
StatePublished - 28 Jun 2017
Externally publishedYes
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: 12 Dec 201715 Dec 2017

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017


Conference56th IEEE Annual Conference on Decision and Control, CDC 2017


FundersFunder number
National Science Foundation
Air Force Office of Scientific Research
Jet Propulsion Laboratory
GoogleAitF-1637598, CCF-1018927, CCF-1409204, CNS-0932428, CCF-1423663
Horizon 2020 Framework Programme
H2020 Marie Skłodowska-Curie Actions708932
King Abdullah University of Science and Technology
King Abdulaziz University


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