NDLI: Duality of Singular Paths for (2, 3, 5)-Distributions

Content Provider	Springer Nature Link
Author	Yuku, Wataru Ishikawa, Goo Kitagawa, Yumiko
Copyright Year	2014
Abstract	We show a duality which arises from distributions of Cartan type, having growth (2, 3, 5), from the viewpoint of geometric control theory. In fact, we consider the space of singular (or abnormal) paths on a given five-dimensional space endowed with a Cartan distribution, which form another five-dimensional space with a cone structure. We regard the cone structure as a control system and show that the space of singular paths of the cone structure is naturally identified with the original space. Moreover, we observe an asymmetry on this duality in terms of singular paths.
Ending Page	171
Page Count	17
Starting Page	155
File Format	PDF
ISSN	10792724
e-ISSN	15738698
Journal	Journal of Dynamical and Control Systems
Issue Number	2
Volume Number	21
Language	English
Publisher	Springer US
Publisher Date	2014-03-21
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Singular control Cone structure Vector distributions (subbundles of the tangent bundles) Vibration, Dynamical Systems, Control Sub-Riemannian geometry Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Analysis Applications of Mathematics Cartan prolongation Differential invariants (local theory), geometric objects
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Algebra and Number Theory Numerical Analysis

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Duality of Singular Paths for (2, 3, 5)-Distributions