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Flat systems, equivalence and trajectory generation 
Abstract 
Flat systems, an important subclass of non … Flat systems, an important subclass of nonlinear control systems introduced
via differentialalgebraic methods, are deﬁned in a differential
geometric framework. We utilize the inﬁnite dimensional geometry developed
by Vinogradov and coworkers: a control system is a diffiety, or more
precisely, an ordinary diffiety, i.e. a smooth inﬁnitedimensional manifold
equipped with a privileged vector ﬁeld. After recalling the deﬁnition of
a LieBacklund mapping, we say that two systems are equivalent if they
are related by a LieBacklund isomorphism. Flat systems are those systems
which are equivalent to a controllable linear one. The interest of
such an abstract setting relies mainly on the fact that the above system
equivalence is interpreted in terms of endogenous dynamic feedback. The
presentation is as elementary as possible and illustrated by the VTOL
aircraft. ible and illustrated by the VTOL
aircraft. +


Authors  Phillipe Martin, Richard Murray, Pierre Rouchon + 
ID  2003d + 
Source  CDS Technical Report + 
Tag  mmr03cds + 
Title  Flat systems, equivalence and trajectory generation + 
Type  Technical Report + 
Categories  Papers 
Modification date This property is a special property in this wiki.

15 May 2016 06:18:44 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/mmr03cds.pdf + 
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Flat systems, equivalence and trajectory generation +  Title 
