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Differential Flatness and Absolute Equivalence of Nonlinear Control Systems 
Abstract 
In this paper we give a formulation of dif … In this paper we give a formulation of differential flatnessa concept originally
introduced by Fleiss, Levine, Martin, and Rouchonin 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. tems and
open questions will be discussed. +


Authors  Michiel van Nieuwstadt, Muruhan Rathinam, Richard M. Murray + 
Flags  NoRequest + 
ID  1994d + 
Source  <i>SIAM J. Control and Optimization</i>, 36(4):12251239 + 
Tag  nrm94cdc + 
Title  Differential Flatness and Absolute Equivalence of Nonlinear Control Systems + 
Type  CDS Technical Report + 
Categories  Papers 
Modification date This property is a special property in this wiki.

15 May 2016 06:20:50 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/nm94cds.pdf + 
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Differential Flatness and Absolute Equivalence of Nonlinear Control Systems +  Title 
