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Feedback Control over a Signal-to-Noise-Ratio Limited Communication Channel

The rapid growth of communications and networking technology has prompted many researchers to study the limitations imposed on a feedback control system by the presence of a communication channel in the feedback loop. The fields of communication and control each have theories of fundamental limitations -- the Shannon theory of reliable communication, and the theory of feedback tradeoffs based on the work of Bode. It is difficult to reconcile these theories because of their different treatment of time delay: delay is detrimental to a feedback system but is required for reliable communication. In joint work with Rick Middleton and Julio Braslavsky, we are motivated by the observation that the bit rate limit in the Shannon theory is derived from properties of an analog AWGN communication channel, specifically its bandwidth and noise and transmission power, or signal to noise ratio (SNR). We thus compute the minimal SNR required to stabilize an unstable plant over a noisy channel. By computing the capacity of a channel with this SNR, we are able to compare our results with those of Nair and Evans, who compute the minimal bit rate required to stabilize over a noise free digital channel. For the state feedback case our results agree, as they do for output feedback with no delay and a minimum phase plant. If NMP zeros or delay is present, the SNR required for stabilization is greater, as one would expect from control practice. Extensions of this work to include performance as well as stabilization have interesting connections to Wiener filtering and to recent work by Martins and Dahleh, which we shall discuss, time permitting.

Type of Seminar:
Public Seminar
Prof. Jim Freudenberg
Department of Electrical Engineering and Computer Science , University of Michigan, Ann Arbor
Nov 13, 2006   14:15

ETH-Zurich, Building ETZ, Room E8, Gloriastrasse 35, Zurich
Contact Person:

Prof. Lino Guzzella
No downloadable files available.
Biographical Sketch:
Jim Freudenberg was born in 1956, and grew up on a farm near Snake Run, Indiana. He received BS degrees in mathematics and physics in 1978, and worked for a year at Rockwell/Collins Avionics, where he designed Kalman filters for aircraft navigation. He then attended the University of Illinois, where he received MS and PhD degrees in electrical engineering, working with Doug Looze. Since 1984 he has been on the faculty of the EECS Department at the University of Michigan, where he is a full professor and a Fellow of the IEEE. His interests are in the theory of fundamental limitations and the teaching of embedded control systems.