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Differential Flatness and Absolute Equivalence

van Nieuwstadt, Michiel and Rathinam, Muruhan and Murray, Richard M. (1995) Differential Flatness and Absolute Equivalence. California Institute of Technology . (Unpublished)

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In this paper we give a formulation of differential flatness---a concept originally introduced by Fleiss, Levine, Martin, and Rouchon---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 differentiable 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 shown 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 will be discussed. Revised 14 Aug 95

Item Type:Report or Paper (Technical Report)
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Murray, Richard M.0000-0002-5785-7481
Additional Information:A preliminary version of this paper appeared in the proceedings of the 1994 Control and Decision Conference. Research supported in part by NASA, by NSF Grant CMS-9502224 and AFOSR Grant F49620-95-0419. 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. The reviewers provided many valuable comments which helped improve several specific results and the overall presentation.
Group:Control and Dynamical Systems Technical Reports
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-95-0419
Classification Code:1991 Mathematics Subject Classification: 93C10; 93B29; 93A05
Record Number:CaltechCDSTR:1995.CIT-CDS-94-006
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Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28005
Deposited By: Tony Diaz
Deposited On:23 Sep 2002
Last Modified:03 Oct 2019 03:28

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