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Differential flatness and absolute equivalence

van Nieuwstadt, M. and Rathinam, M. and Murray, R. M. (1994) Differential flatness and absolute equivalence. In: Proceedings of 1994 33rd IEEE Conference on Decision and Control. Vol.1. IEEE , Piscataway, NJ, pp. 326-332. ISBN 0-7803-1968-0. http://resolver.caltech.edu/CaltechAUTHORS:20190319-091908577

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Abstract

In this paper we give a formulation of differential flatness-a concept originally introduced by Fliess, Levine, Martin, and Rouchon (1992)-in terms of absolute equivalence between exterior differential systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was given in the context of differential algebra, and required that all mappings be meromorphic functions. Our formulation of flatness does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems. In particular, we show that in the case of single input control systems (i.e., codimension 2 Pfaffian systems), a system is differentially flat if and only if it is feedback linearizable via static state feedback. However, in higher codimensions feedback linearizability and flatness are not equivalent: one must be careful with the role of time as well the use of prolongations which may not be realizable as dynamic feedbacks in a control setting. Applications of differential flatness to nonlinear control systems and open questions are also discussed.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/CDC.1994.410908DOIArticle
http://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-94-006Related ItemTechnical Report
ORCID:
AuthorORCID
Murray, R. M.0000-0002-5785-7481
Additional Information:© 1994 IEEE. Research supported in part by NASA. Research supported in part by the Powell Foundation. The authors would like to thank Willem Sluis for many fruitful and inspiring discussions and for introducing us to Cartan’s work and its applications to control theory. We also thank Shankar Sastry for valuable comments on this paper, and Philippe Martin for several useful discussions which led to a more complete understanding of the relationship between endogenous feedback and differential flatness.
Funders:
Funding AgencyGrant Number
NASAUNSPECIFIED
Charles Lee Powell FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20190319-091908577
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190319-091908577
Official Citation:M. van Nieuwstadt, M. Rathinam and R. M. Murray, "Differential flatness and absolute equivalence," Proceedings of 1994 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, USA, 1994, pp. 326-332 vol.1. doi: 10.1109/CDC.1994.410908
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93957
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:19 Mar 2019 16:31
Last Modified:19 Mar 2019 16:31

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