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Flat systems, equivalence and trajectory generation

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Phillipe Martin, Richard Murray, Pierre Rouchon

CDS Technical Report

Flat systems, an important subclass of nonlinear control systems introduced
via differential-algebraic 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 inﬁnite-dimensional manifold
equipped with a privileged vector ﬁeld. After recalling the deﬁnition of
a Lie-Backlund mapping, we say that two systems are equivalent if they
are related by a Lie-Backlund 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.

Technical
Report (PDF, 79 pages, 796K)

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Richard Murray
(murray@cds. caltech.edu)