Needle variations that cannot be summed

Rosa Maria Bianchini, Matthias Kawski

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This article analyzes sets of higher order tangent vectors to reachable sets of analytic control systems (affine in the control). Both small-time local output controllability and small-time local controllability about a nonstationary reference trajectory are considered. In a series of purposefully constructed examples it is shown that the cones generated by needle variations may fail to be convex. The examples demonstrate that the usual technical condition that needle variations must be movable is essential to guarantee desirable convexity properties. Moreover, new doubts are cast on the structural stability of controllability properties, as apparently higher order perturbations can reverse the (lack of) controllability of lower order nilpotent approximating systems, thereby providing new insights about the ultimate question of whether controllability is finitely determined.

Original languageEnglish (US)
Pages (from-to)218-238
Number of pages21
JournalSIAM Journal on Control and Optimization
Volume42
Issue number1
DOIs
StatePublished - 2003

Fingerprint

Controllability
Needles
Higher Order
Local Controllability
Tangent vector
Reachable Set
Structural Stability
Local Time
Convexity
Reverse
Cone
Control System
Trajectory
Cones
Perturbation
Trajectories
Series
Output
Control systems
Demonstrate

Keywords

  • Control variations
  • Nonlinear controllability
  • Optimality
  • Tangent cones

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Control and Optimization

Cite this

Needle variations that cannot be summed. / Bianchini, Rosa Maria; Kawski, Matthias.

In: SIAM Journal on Control and Optimization, Vol. 42, No. 1, 2003, p. 218-238.

Research output: Contribution to journalArticle

Bianchini, Rosa Maria ; Kawski, Matthias. / Needle variations that cannot be summed. In: SIAM Journal on Control and Optimization. 2003 ; Vol. 42, No. 1. pp. 218-238.
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