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Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information

Martins, Nuno C. and Dahleh, Munther A. and Doyle, John C. (2007) Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information. IEEE Transactions on Automatic Control, 52 (1). pp. 56-66. ISSN 0018-9286. doi:10.1109/TAC.2006.887898.

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In this paper, we study fundamental limitations of disturbance attenuation of feedback systems, under the assumption that the controller has a finite horizon preview of the disturbance. In contrast with prior work, we extend Bode's integral equation for the case where the preview is made available to the controller via a general, finite capacity, communication system. Under asymptotic stationarity assumptions, our results show that the new fundamental limitation differs from Bode's only by a constant, which quantifies the information rate through the communication system. In the absence of asymptotic stationarity, we derive a universal lower bound which uses Shannon's entropy rate as a measure of performance. By means of a case-study, we show that our main bounds may be achieved.

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Doyle, John C.0000-0002-1828-2486
Additional Information:© 2007 IEEE. Manuscript received October 17, 2005; revised May 15, 2006 and June 2, 2006. [Posted online: 2007-01-15] E. Jonckheere. This work was sponsored by the UCLA, MURI project title: “Cooperative Control of Distributed Autonomous Vehicles in Adversarial Environments,” award 0205-G-CB222. The work of N.C. Martins was supported by the Portuguese Foundation for Science and Technology and the European Social Fund, PRAXIS SFRH/BPD/19008/2004/JS74. The authors would like to thank O. Ayaso (M.I.T.), J. Goncalves (Cambridge Univ., U.K.), and M. Khammash (UCSB) for providing references to examples in Biology. They also would like to express our gratitude to P. Narayan (Univ. Maryland) for carefully reading their first manuscript, to J. Chen (Univ. California, Riverside) for pointing us to a few references in Preview Control and to S.K. Mitter (M.I.T.) for interesting discussions. They are also grateful to the Associate Editor and to the reviewers for their feedback and suggestions, which have greatly improved the quality of this paper.
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Fundação para a Ciência e a Tecnologia (FCT)UNSPECIFIED
European Social FundSFRH/BPD/19008/2004/JS74
Subject Keywords:Fundamental limits, information constraints, preview control
Issue or Number:1
Record Number:CaltechAUTHORS:MARieeetac07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7401
Deposited By: Archive Administrator
Deposited On:09 Feb 2007
Last Modified:08 Nov 2021 20:42

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