Signal detection and approximate adaptation implies an approximate internal model

Burton W. Andrews; Pablo A. Iglesias; Eduardo D. Sontag

doi:10.1109/cdc.2006.377227

Signal detection and approximate adaptation implies an approximate internal model

Burton W. Andrews, Pablo A. Iglesias, Eduardo D. Sontag

Whiting School of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Scopus citations

Abstract

The proper function of many biological systems requires that external perturbations be detected, allowing the system to adapt to these environmental changes. It is now well established that this dual detection and adaptation requires that the system have an internal model in the feedback loop. In this paper we relax the requirement that the response of the system adapt perfectly, but instead allow regulation to within a neighborhood of zero. We show that linear systems with the ability to detect input signals and approximately adapt require an approximate model of the input. We illustrate our results by analyzing two well-studied biological systems.

Original language	English (US)
Title of host publication	Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2364-2369
Number of pages	6
ISBN (Print)	1424401712, 9781424401710
DOIs	https://doi.org/10.1109/cdc.2006.377227
State	Published - 2006
Event	45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: Dec 13 2006 → Dec 15 2006

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	45th IEEE Conference on Decision and Control 2006, CDC
Country/Territory	United States
City	San Diego, CA
Period	12/13/06 → 12/15/06

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/cdc.2006.377227

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Andrews, B. W., Iglesias, P. A., & Sontag, E. D. (2006). Signal detection and approximate adaptation implies an approximate internal model. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC (pp. 2364-2369). Article 4177419 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/cdc.2006.377227

Signal detection and approximate adaptation implies an approximate internal model. / Andrews, Burton W.; Iglesias, Pablo A.; Sontag, Eduardo D.
Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc., 2006. p. 2364-2369 4177419 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Andrews, BW, Iglesias, PA & Sontag, ED 2006, Signal detection and approximate adaptation implies an approximate internal model. in Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC., 4177419, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2364-2369, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 12/13/06. https://doi.org/10.1109/cdc.2006.377227

Andrews BW, Iglesias PA, Sontag ED. Signal detection and approximate adaptation implies an approximate internal model. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc. 2006. p. 2364-2369. 4177419. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/cdc.2006.377227

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AB - The proper function of many biological systems requires that external perturbations be detected, allowing the system to adapt to these environmental changes. It is now well established that this dual detection and adaptation requires that the system have an internal model in the feedback loop. In this paper we relax the requirement that the response of the system adapt perfectly, but instead allow regulation to within a neighborhood of zero. We show that linear systems with the ability to detect input signals and approximately adapt require an approximate model of the input. We illustrate our results by analyzing two well-studied biological systems.

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Signal detection and approximate adaptation implies an approximate internal model

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