Nonlinear control and Lie-Backlund transformations: towards a new differential geometric standpoint

Author

Fliess, Michel ; Tevine, J. ; Martin, Philippe ; Rouchon, Pierre

Author_Institution

Lab. des Signaux et Syst., CNRS, Gif-sur-Yvette, France

Volume

1

fYear

1994

Firstpage

339

Abstract

Nonlinear control is related to Lie-Backlund transformation of some infinite-dimensional manifolds. State-variable representations, feedback and, especially, dynamic feedback linearization, i.e., flatness, are briefly examined, as well as the relationship with the differential algebraic approach. This setting provides a most natural framework for time scalings. We indicate via the carlike robot how to utilize this new time for stabilizing around a trajectory a driftless flat system

Keywords

Lie algebras; differential geometry; feedback; linearisation techniques; nonlinear control systems; transforms; Lie-Backlund transformations; car-like robot; differential algebra; differential geometric standpoint; driftless flat system; dynamic feedback linearization; flatness; infinite-dimensional manifolds; nonlinear control; stabilization; state-variable representations; time scalings; Algebra; Automatic control; Computational geometry; Control systems; Manifolds; Nonlinear dynamical systems; Partial differential equations; Physics; Robots; State feedback;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on

Conference_Location

Lake Buena Vista, FL

Print_ISBN

0-7803-1968-0

Type

conf

DOI

10.1109/CDC.1994.410906

Filename

410906