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A matrix Lie group of Carnot type for filiform subRiemannian structures and its application

Summary: A matrix Lie group of Carnot type for filiform
sub­Riemannian structures and its application
to control systems in chained form
Claudio Altafini \Lambda
Optimization and Systems Theory
Royal Institute of Technology
SE­10044, Stockholm, Sweden
tel. +46 8 790 7507
fax +46 8 225 320
March 13, 2000
A Carnot group G is a simply connected graded nilpotent Lie group
endowed a left­invariant distribution generating the Lie algebra g of G.
Here we show that the quotient manifold of a filiform Carnot group by
the subgroup generated by its characteristic line field is projectively
abelian. The result is used to show how a class of bilinear control
systems have an intrinsic linear behavior.
1 Introduction and motivation
The kinematic model of an n­trailer i.e. a car­like vehicle pulling an arbitrary


Source: Altafini, Claudio - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)


Collections: Engineering; Mathematics