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Is it possible to recognize Local Controllability in a
 

Summary: Chapter 1
Is it possible to recognize
Local Controllability in a
nite number of
di erentiations?
Andrei A. Agrachev
Steklov Mathematical Institute
ul. Gubkina 8
Moscow 117966
RUSSIA
agrachev@mi.ras.ru
1.1 Description of the problem
Let f 1 ; : : : ; f k ; k  2, be real{analytic vector elds de ned on a neighbor-
hood of the origin in R n , and t > 0. The point x 2 R n is called attainable
from the origin for a time less than t and with no more than N switch-
ings, if there exists a subdivision 0 = t 0 < t 1 < : : : < t N+1 < t of the
segment [0; t] and solutions  j (t), t 2 [t j ; t j+1 ] of the di erential equations
_
x = f i j
(x), for some i j 2 f1; : : : ; kg, such that  0 (0) = 0,  j 1 (t j ) =  j (t j )

  

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

 

Collections: Engineering; Mathematics