The Minimal Directed Information Needed to Improve the LQG Cost

Oron Sabag, Peida Tian, Victoria Kostina, Babak Hassibi

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

8 Scopus citations


We study a linear quadratic Gaussian (LQG) control problem, in which a noisy observation of the system state is available to the controller. To lower the achievable LQG cost, we introduce an extra communication link from the system to the controller. We investigate the trade-off between the improved LQG cost and the consumed communication (information) resources that are measured with the conditional directed information. The objective is to minimize the directed information over all encoding-decoding policies subject to a constraint on the LQG cost. The main result is a semidefinite programming formulation for the optimization problem in the finite-horizion scenario where the dynamical system may have time-varying parameters. This result extends the seminal work by Tanaka et al., where the direct noisy measurement of the system state at the controller is assumed to be absent. As part of our derivation to show the optimality of an encoder that transmits a Gaussian measurement of the state, we show that the presence of the noisy measurements at the encoder can not reduce the minimal directed information, extending a prior result of Kostina and Hassibi to the vector case. Finally, we show that the results in the finite-horizon case can be extended to the infinite-horizon scenario when assuming a time-invariant system, but possibly a time-varying policy. We show that the solution for this optimization problem can be realized by a time-invariant policy whose parameters can be computed explicitly from a finite-dimensional semidefinite program.

Original languageEnglish
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Electronic)9781728174471
StatePublished - 14 Dec 2020
Externally publishedYes
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: 14 Dec 202018 Dec 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference59th IEEE Conference on Decision and Control, CDC 2020
Country/TerritoryKorea, Republic of
CityVirtual, Jeju Island

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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