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

Abstract
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.

Citation
Khina, A., Kostina, V., Khisti, A., & Hassibi, B. (2019). Tracking and Control of Gauss–Markov Processes over Packet-Drop Channels with Acknowledgments. IEEE Transactions on Control of Network Systems, 6(2), 549–560. doi:10.1109/tcns.2018.2850225

Acknowledgements
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.

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
IEEE Transactions on Control of Network Systems

DOI
10.1109/TCNS.2018.2850225

Additional Links
https://ieeexplore.ieee.org/document/8395023/

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