Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
METHODS OF CONTROL THEORY IN NONHOLONOMIC GEOMETRY
 

Summary: METHODS OF CONTROL THEORY
IN NONHOLONOMIC GEOMETRY
Andrei A. Agrachev
1.Introduction. Let M be a C
-manifold and TM the total space of the tangent
bundle. A control system is a subset V TM. Fix an initial point q0 M and a
segment [0, t] R. Admissible trajectories are Lipschitzian curves q(), 0
t, q(0) = q0, satisfying a differential equation of the form
(1) q = v (q),
where v (q) V TqM, q M, v (q) is smooth in q, bounded and measurable
in . The mapping q() q(t) which maps admissible trajectories in their end
points is called an end-point mapping.
Control Theory is in a sense a theory of end-point mappings. This point
of view is rather restrictive but sufficient for our purposes. For instance, attain-
able sets are just images of end-point mappings. Geometric Control Theory tends
to characterize properties of these mappings in terms of iterated Lie brackets of
smooth vector fields on M with values in V. A number of researchers have shown
a remarkable ingenuity in this regard leading to encouraging results. See, for in-
stance, books [1],[2],[3] to get an idea of various periods in the development of this
domain and for other references. A complete list of references would probably run

  

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

 

Collections: Engineering; Mathematics