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Feedback Stabilization Over Signal-to-Noise Ratio Constrained Channels.

Braslavsky, Julio H. and Middleton, Richard H. and Freudenberg, James S. (2007) Feedback Stabilization Over Signal-to-Noise Ratio Constrained Channels. IEEE Transactions on Automatic Control, 52 (8). pp. 1391-1403. ISSN 0018-9286

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Abstract

There has recently been significant interest in feedback stabilization problems with communication constraints including constraints on the available data rate. Signal-to-noise ratio (SNR) constraints are one way in which data-rate limits arise, and are the focus of this paper. In both continuous and discrete-time settings, we showthat there are limitations on the ability to stabilize an unstable plant over a SNR constrained channel using finite-dimensional linear time invariant (LTI) feedback. In the case of state feedback, or output feedback with a delay-free, minimum phase plant, these limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity data rate over the same channel. In the case of LTI output feedback, additional limitations are shown to apply if the plant is nonminimum phase. In this case, we show that for a continuous-time nonminimum phase plant, a periodic linear time varying feedback scheme with fast sampling may be used to recover the original SNR requirement at the cost of robustness properties. The proposed framework inherently captures channel noise effects in a simple formulation suited to conventional LTI control performance and robustness analysis, and has potential to handle time delays and bandwidth constraints in a variety of control over communication links problems.

Item Type: Article
Additional Information: "©2007 IEEE. Reprinted from IEEE Transactions on Automatic Control. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE." http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4287133&isnumber=4287128
Keywords: Continuous time systems; Delays; Discrete time systems; Feedback; Robust control; Telecommunication channels; Telecommunication control; Telecommunication links; Signal-to-noise ratio (SNR); SNR constrained channel; Shannon capacity data rate; Communication constraints; Communication links; Continuous time system; Continuous-time nonminimum phase plant; Discrete time system; Feedback stabilization; Finite-dimensional linear time invariant feedback; time delays; Communication channels; Control systems; Feedback communication; Information rates; Linear-quadratic-Gaussian control; Networked control systems; Hamilaton Institute.
Subjects: Science & Engineering > Hamilton Institute
Science & Engineering > Computer Science
Item ID: 1741
Identification Number: 10.1109/TAC.2007.902739
Depositing User: Hamilton Editor
Date Deposited: 14 Dec 2009 10:55
Journal or Publication Title: IEEE Transactions on Automatic Control
Publisher: IEEE
Refereed: Yes
URI:

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