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Published December 2005 | Published
Book Section - Chapter Open

Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information

Abstract

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 stationarity, we derive a universal lower bound which uses entropy rates as a measure of performance.

Additional Information

© 2005 IEEE. The authors would like to thank Ola Ayaso (MIT), Jorge Goncalves (Cambridge U., U.K.) and Mustafa Khammash (UCSB) for providing references to examples in Biology. We also would like to express our gratitude to Prakash Narayan (U. Maryland) for carefully reading our first manuscript, to Sanjoy Mitter (MIT) for interesting suggestions and to Jie Chen (U California Riverside) for pointing us to a few references in Preview Control. This work was sponsored by the UCLA, MURI project title: "Cooperative Control of Distributed Autonomous Vehicles in Adversarial Environments", award: 0205-G-CB222. Nuno C. Martins was supported by the Portuguese Foundation for Science and Technology and the European Social Fund, PRAXIS SFRH/BPD/19008/2004/JS74.

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