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Flat systems, equivalence and trajectory generation

Martin, Phillipe and Murray, Richard M. and Rouchon, Pierre (2003) Flat systems, equivalence and trajectory generation. California Institute of Technology . (Unpublished)

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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.

Item Type:Report or Paper (Technical Report)
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Murray, Richard M.0000-0002-5785-7481
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:2003.008
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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:28021
Deposited By: Imported from CaltechCDSTR
Deposited On:29 Jul 2003
Last Modified:03 Oct 2019 03:28

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