An Analogue of Shannon Information Theory for Detection and Stabilization via Noisy Discrete Communication Channels

The paper addresses both detection and stabilization problems involving communication errors and capacity constraints. Discrete-time partially observed linear systems are studied. Unlike the classic theory, the sensor signals are transmitted to the estimator/controller over a noisy digital communica...

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Published in:SIAM journal on control and optimization Vol. 46; no. 4; pp. 1323 - 1367
Main Authors: Matveev, Alexey S., Savkin, Andrey V.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2007
Subjects:
Codes
Communication channels
Control theory
Controllers
Eigenvalues
Inequality
Information theory
Noise
ISSN:0363-0129, 1095-7138
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Abstract The paper addresses both detection and stabilization problems involving communication errors and capacity constraints. Discrete-time partially observed linear systems are studied. Unlike the classic theory, the sensor signals are transmitted to the estimator/controller over a noisy digital communication link modeled as a stochastic stationary discrete memoryless channel. It is shown that for noise-free plants, the Shannon capacity of the channel constitutes the border separating the cases where stabilization and reliable detection (asymptotic state estimation) with arbitrarily large probability are and are not possible, respectively.
AbstractList The paper addresses both detection and stabilization problems involving communication errors and capacity constraints. Discrete-time partially observed linear systems are studied. Unlike the classic theory, the sensor signals are transmitted to the estimator/controller over a noisy digital communication link modeled as a stochastic stationary discrete memoryless channel. It is shown that for noise-free plants, the Shannon capacity of the channel constitutes the border separating the cases where stabilization and reliable detection (asymptotic state estimation) with arbitrarily large probability are and are not possible, respectively.
Author Savkin, Andrey V.
Matveev, Alexey S.
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Communication channels
Control theory
Controllers
Eigenvalues
Inequality
Information theory
Noise
Title An Analogue of Shannon Information Theory for Detection and Stabilization via Noisy Discrete Communication Channels
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