Flat systems, equivalence and trajectory generation

Abstract

Flat systems, an important subclass of nonlinear control systems introduced
\nvia differential-algebraic methods, are defined in a differential
\ngeometric framework. We utilize the infinite dimensional geometry developed
\nby Vinogradov and coworkers: a control system is a diffiety, or more
\nprecisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold
\nequipped with a privileged vector field. After recalling the definition of
\na Lie-Backlund mapping, we say that two systems are equivalent if they
\nare related by a Lie-Backlund isomorphism. Flat systems are those systems
\nwhich are equivalent to a controllable linear one. The interest of
\nsuch an abstract setting relies mainly on the fact that the above system
\nequivalence is interpreted in terms of endogenous dynamic feedback. The
\npresentation is as elementary as possible and illustrated by the VTOL
\naircraft.
\n