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

Published online by Cambridge University Press:  15 August 2002

Mikhail Krastanov  and
Marc Quincampoix
Mikhail Krastanov
Affiliation:
Institute of Mathematics and Informatics, Acad. G. Bonchev Str., Bl. 8, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria; krast@bas.bg.
Marc Quincampoix
Affiliation:
Département de Mathématiques, Université de Bretagne Occidentale, 6 avenue Victor Le Gorgeu, BP. 809, 29285 Brest Cedex, France; Marc.Quincampoix@univ-brest.fr.
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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.

Keywords

Attainabilitycontrolabilitylocal variationspolynomial controllinear controls.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 499 - 516
Copyright
© EDP Sciences, SMAI, 2001

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