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Algorithms for Optimal Control with Fixed-Rate Feedback

Khina, Anatoly and Nakahira, Yorie and Su, Yu and Yildiz, Hikmet and Hassibi, Babak (2018) Algorithms for Optimal Control with Fixed-Rate Feedback. . (Unpublished)

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We consider a discrete-time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimize performance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions and sequential Bayesian filtering to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions and rate-limited time-varying noiseless channels. We further extend the framework to event-triggered control by allowing to convey information via an additional "silent symbol", i.e., by avoiding transmitting bits; by constraining the minimal probability of silence we attain a tradeoff between the transmission rate and the control cost for rates below one bit per sample.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Khina, Anatoly0000-0003-2359-1678
Nakahira, Yorie0000-0003-3324-4602
Yildiz, Hikmet0000-0002-0891-3352
Additional Information:This work was done, in part, while A. Khina was visiting the Simons Institute for the Theory of Computing. This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 708932. The work of Y. Nakahira was funded by grants from AFOSR and NSF, and gifts from Cisco, Huawei, and Google. The work of Y. Su was supported in part by NSF through AitF-1637598. The work of B. Hassibi was supported in part by the National Science Foundation under Grant CNS-0932428, Grant CCF-1018927, Grant CCF-1423663, and Grant CCF-1409204; in part by a grant from Qualcomm Inc.; in part by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund; and in part by King Abdullah University of Science and Technology. The material in this paper was presented in part at the IEEE Conference on Decision and Control, Melbourne, VIC, Australia, Dec., 2017. A. Khina thanks M. J. Khojasteh and M. Franceschetti for many stimulating and helpful discussions, and especially for introducing him to event-triggered control and pointing his attention to [9]–[12].
Funding AgencyGrant Number
Marie Curie Fellowship708932
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
JPL President and Director’s FundUNSPECIFIED
King Abdullah University of Science and Technology (KAUST)UNSPECIFIED
Subject Keywords:Networked control, linear quadratic Gaussian control, event-triggered control, quantization
Record Number:CaltechAUTHORS:20190402-085532839
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94357
Deposited By: Tony Diaz
Deposited On:02 Apr 2019 17:11
Last Modified:04 Dec 2019 21:38

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