ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - 2001 - Volume 6  

Research Article

Local small time controllability and attainability of a set for nonlinear control system

Krastanov, Mikhaila1 and Quincampoix, Marca2

a1 Institute of Mathematics and Informatics, Acad. G. Bonchev Str., Bl. 8, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria; krast@bas.bg.

a2 Département de Mathématiques, Université de Bretagne Occidentale, 6 avenue Victor Le Gorgeu, BP. 809, 29285 Brest Cedex, France; Marc.Quincampoix@univ-brest.fr.

Abstract

In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set is a hyperplane.

(Received September 7 2000)

(Received March 2001)

(Online publication August 15 2002)

Key Words:

  • Attainability;
  • controlability;
  • local variations;
  • polynomial control;
  • linear controls.

Mathematics Subject Classification:

  • 93B05;
  • 93B03;
  • 93C05;
  • 93C10;
  • 49J53