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 (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220804-201321456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) | ||||||||
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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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