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Approximate Reduction of Dynamical Systems

Tabuada, Paulo and Ames, Aaron D. and Julius, Agung and Pappas, George (2006) Approximate Reduction of Dynamical Systems. In: Proceedings of the 45th IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 6408-6413. ISBN 1-4244-0171-2. https://resolver.caltech.edu/CaltechAUTHORS:20170510-174336817

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Abstract

The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction is typically performed in an "exact" manner - as is the case with mechanical systems with symmetry - which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a lower dimensional space. These concepts are illustrated on a series of examples.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/CDC.2006.377156DOIArticle
https://arxiv.org/abs/0707.3804arXivDiscussion Paper
ORCID:
AuthorORCID
Tabuada, Paulo0000-0002-3417-0951
Additional Information:© 2006 IEEE. This research was partially supported by the National Science Foundation, EHS award 0509313 and CCR award 0225610.
Funders:
Funding AgencyGrant Number
NSFEHS-0509313
NSFCCR-0225610
Record Number:CaltechAUTHORS:20170510-174336817
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170510-174336817
Official Citation:P. Tabuada, A. D. Ames, A. Julius and G. Pappas, "Approximate Reduction of Dynamical Systems," Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, 2006, pp. 6408-6413. doi: 10.1109/CDC.2006.377156
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77361
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:16 May 2017 19:47
Last Modified:03 Oct 2019 17:56

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