Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
The 37th IEEE Conference on Decision and Control, Tampa, Florida, December 1998. On the Equivalence of Di erent Types of Local Minima in
 

Summary: The 37th IEEE Conference on Decision and Control, Tampa, Florida, December 1998.
On the Equivalence of Di erent Types of Local Minima in
Sub-Riemannian Problems
Andrei A. Agrachev
Steklov Mathematical Institute, 8 ul. Gubkina, Moscow 117966
E-mail: agrachev@mi.ras.ru
Abstract|Sub-Riemannian problems are under in-
tensive study in 90-th. They are typical optimal
control problems admitting singular and abnormal
minimizers (see [1 { 5]). Moreover, any singular
geodesic in the sub-Riemannian problem is abnor-
mal and vice versa.
So minimizers may be singular geodesics, but it
is not clear for today, may they have singularities
as curves in the state space or not. Until now,
all known minimizers were smooth. In this pa-
per we compare di erent types of local minimal-
ity for smooth admissible curves. Surprisingly, the
smoothness of the trajectory implies the equivalence
of local minimality in rather di erent topologies.

  

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

 

Collections: Engineering; Mathematics