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Optimal Signal to Noise Ratio in Feedback over Communication Channels with Memory

Rojas, A.J. and Freudenberg, J.S. and Braslavsky, J.H. and Middleton, R.H. (2006) Optimal Signal to Noise Ratio in Feedback over Communication Channels with Memory. In: 45th IEEE Conference on Decision & Control Manchester Grand Hyatt Hotel San Diego, CA, USA, December 13-15, 2006. IEEE, pp. 1129-1134. ISBN 1-4244-0171-2

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Abstract

Communication channels impose a number of obstacles to feedback control, such as delay, noise, and constraints in communication data-rate. One alternate line of recent work considers the problem of feedback stabilization subject to a constraint in the signal-to-noise ratio (SNR). It has been shown for continuous-time systems that the optimal control problem arising in achieving minimal SNR can be formulated as a linear quadratic Gaussian (LQG) control problem with weights chosen as in the loop transfer recovery (LTR) technique. The present paper extends such LQG/LTR formulation to discretetime systems with feedback over channels with memory. By using such formulation, we derive exact expressions for the LTI controller and loop sensitivity functions that achieve minimal SNR under the effect of time-delay, non minimum phase zeros and colored additive noise. For the minimum-phase case with white noise and no time delay, we show that the optimal feedback loop obtained after applying LTR has a structure equivalent to that of a communication channel with feedback from the output to the input.

Item Type: Book Section
Additional Information: "©2006 IEEE. Reprinted from the 45th IEEE Conference on Decision & Control Manchester Grand Hyatt Hotel San Diego, CA, USA, December 13-15, 2006. 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=4178027&isnumber=4176993
Keywords: Continuous time systems; Discrete time systems; Feedback; Linear quadratic Gaussian control; Optimal control; Stability; Telecommunication channels; Communication channels; Feedback control; Feedback stabilization; Loop sensitivity functions; Loop transfer recovery; Optimal control; CDC 2006; Hamilton Institute.
Subjects: Science & Engineering > Hamilton Institute
Science & Engineering > Computer Science
Item ID: 1789
Identification Number: 10.1109/CDC.2006.377171
Depositing User: Hamilton Editor
Date Deposited: 18 Jan 2010 13:34
Publisher: IEEE
Refereed: Yes
URI:

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