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The Minimal Directed Information Needed to Improve the LQG Cost

Sabag, Oron and Tian, Peida and Kostina, Victoria and Hassibi, Babak (2020) The Minimal Directed Information Needed to Improve the LQG Cost. In: 2020 59th IEEE Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 1842-1847. ISBN 9781728174471. https://resolver.caltech.edu/CaltechAUTHORS:20210121-152557490

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Abstract

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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/cdc42340.2020.9304490DOIArticle
ORCID:
AuthorORCID
Sabag, Oron0000-0002-7907-1463
Tian, Peida0000-0003-3665-8173
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2020 IEEE. This work was supported in part by the National Science Foundation (NSF) under grants CCF-1751356 and CCF-1956386. The work of O. Sabag is partially supported by the ISEF international postdoctoral fellowship.
Funders:
Funding AgencyGrant Number
NSFCCF-1751356
NSFCCF-1956386
ISEF FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20210121-152557490
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210121-152557490
Official Citation:O. Sabag, P. Tian, V. Kostina and B. Hassibi, "The Minimal Directed Information Needed to Improve the LQG Cost," 2020 59th IEEE Conference on Decision and Control (CDC), Jeju Island, Korea (South), 2020, pp. 1842-1847, doi: 10.1109/CDC42340.2020.9304490
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107638
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:22 Jan 2021 20:13
Last Modified:22 Jan 2021 20:13

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