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

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 er...

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Veröffentlicht in:IEEE transactions on control of network systems Jg. 6; H. 2; S. 549 - 560
Hauptverfasser: Khina, Anatoly, Kostina, Victoria, Khisti, Ashish, Hassibi, Babak
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Piscataway IEEE 01.06.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Control systems
Delay
Gaussian process
Hafnium
Linear quadratic Gaussian control
Markov analysis
Markov processes
Networked control systems
Optimization
packet loss
Reactive power
sequential coding of correlated sources
source coding with side information
state estimation
successive refinement
Tracking control
Two dimensional displays
ISSN:2325-5870, 2372-2533
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2018.2850225