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Reducing the LQG Cost with Minimal Communication

Sabag, Oron and Tian, Peida and Kostina, Victoria and Hassibi, Babak (2021) Reducing the LQG Cost with Minimal Communication. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220804-201321456

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Abstract

We study the linear quadratic Gaussian (LQG) control problem, in which the controller's observation of the system state is such that a desired cost is unattainable. To achieve the desired LQG cost, we introduce a communication link from the observer (encoder) to the controller. We investigate the optimal trade-off between the improved LQG cost and the consumed communication (information) resources, measured with the conditional directed information, across all encoding-decoding policies. The main result is a semidefinite programming formulation for that optimization problem in the finite-horizon scenario, which applies to time-varying linear dynamical systems. This result extends a seminal work by Tanaka et al., where the only information the controller knows about the system state arrives via a communication channel, to the scenario where the controller has also access to a noisy observation of the system state. As part of our derivation to show the optimiality of an encoder that transmits a memoryless Gaussian measurement of the state, we show that the presence of the controller's observations at the encoder can not reduce the minimal directed information. For time-invariant systems, where the optimal policy may be time-varying, we show in the infinite-horizon scenario that the optimal policy is time-invariant and can be computed explicitly from a solution of a finite-dimensional semidefinite programming. The results are demonstrated via examples that show that even low-quality measurements can have a significant impact on the required communication resources.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2109.12246arXivDiscussion Paper
ORCID:
AuthorORCID
Sabag, Oron0000-0002-7907-1463
Tian, Peida0000-0003-3665-8173
Kostina, Victoria0000-0002-2406-7440
Additional Information:Attribution 4.0 International (CC BY 4.0)
Record Number:CaltechAUTHORS:20220804-201321456
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220804-201321456
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116135
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:11 Aug 2022 23:37
Last Modified:11 Aug 2022 23:37

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