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Tracking and Control of Gauss-Markov Processes over Packet-Drop Channels with Acknowledgments

Khina, Anatoly and Kostina, Victoria and Khisti, Ashish and Hassibi, Babak (2019) Tracking and Control of Gauss-Markov Processes over Packet-Drop Channels with Acknowledgments. IEEE Transactions on Control of Network Systems, 6 (2). pp. 549-560. ISSN 2325-5870.

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We consider the problem of tracking the state of Gauss–Markov processes over rate-limited erasure-prone links. We concentrate first on the scenario in which several independent processes are seen by a single observer. The observer maps the processes into finite-rate packets that are sent over the erasure-prone links to a state estimator, and are acknowledged upon packet arrivals. The aim of the state estimator is to track the processes with zero delay and with minimum mean square error (MMSE). We show that, in the limit of many processes, greedy quantization with respect to the squared error distortion is optimal. That is, there is no tension between optimizing the MMSE of the process in the current time instant and that of future times. For the case of packet erasures with delayed acknowledgments, we connect the problem to that of compression with side information that is known at the observer and may be known at the state estimator—where the most recent packets serve as side information that may have been erased, and demonstrate that the loss due to a delay by one time unit is rather small. For the scenario where only one process is tracked by the observer–state estimator system, we further show that variable-length coding techniques are within a small gap of the many-process outer bound. We demonstrate the usefulness of the proposed approach for the simple setting of discrete-time scalar linear quadratic Gaussian control with a limited data-rate feedback that is susceptible to packet erasures.

Item Type:Article
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URLURL TypeDescription Paper
Khina, Anatoly0000-0003-2359-1678
Kostina, Victoria0000-0002-2406-7440
Khisti, Ashish0000-0002-2331-8965
Additional Information:© 2018 IEEE. Manuscript received October 27, 2017; revised May 17, 2018; accepted June 1, 2018. Date of publication June 25, 2018; date of current version May 28, 2019. This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant 708932. The work of V. Kostina was supported in part by the National Science Foundation under Grant CCF-1566567 and Grant CCF-1751356. The work of A. Khisti was supported by the Canada Research Chairs Program. 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. Recommended by Associate EditorM. Rabbat. This work was done in part while A. Khina and V. Kostina were visiting the Simons Institute for the Theory of Computing. This paper was presented in part at the IEEE Information Theory Workshop, Kaohsiung, Taiwan, November 2017.
Funding AgencyGrant Number
Marie Curie Fellowship708932
Canada Research Chairs ProgramUNSPECIFIED
JPL President and Director's FundUNSPECIFIED
King Abdullah University of Science and Technology (KAUST)UNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20180629-113827049
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Official Citation:A. Khina, V. Kostina, A. Khisti and B. Hassibi, "Tracking and Control of Gauss–Markov Processes over Packet-Drop Channels with Acknowledgments," in IEEE Transactions on Control of Network Systems, vol. 6, no. 2, pp. 549-560, June 2019. doi: 10.1109/TCNS.2018.2850225
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87474
Deposited By: Tony Diaz
Deposited On:29 Jun 2018 20:03
Last Modified:03 Oct 2019 19:56

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