Rate-cost tradeoffs in control

Victoria Kostina, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Scopus citations

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.
Original languageEnglish (US)
Title of host publication2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages1157-1164
Number of pages8
ISBN (Print)9781509045501
DOIs
StatePublished - Feb 13 2017
Externally publishedYes

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