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Symmetry, Integrability and Geometry: Methods and Applications, 2013, Volume 9, 034, 31 pp.
DOI: https://doi.org/10.3842/SIGMA.2013.034 (Mi sigma817) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Geometry of Optimal Control for Control-Affine Systems

Jeanne N. Clellanda, Christopher G. Moseleyb, George R. Wilkensc

a Department of Mathematics, 395 UCB, University of Colorado, Boulder, CO 80309-0395, USA
b Department of Mathematics and Statistics, Calvin College, Grand Rapids, MI 49546, USA
c Department of Mathematics, University of Hawaii at Manoa, 2565 McCarthy Mall, Honolulu, HI 96822-2273, USA
Full-text PDF (494 kB) Citations (4)
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DOI: https://doi.org/10.3842/SIGMA.2013.034
Abstract: Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied.
Keywords: affine distributions; optimal control theory; Cartan's method of equivalence.
Received: June 7, 2012; in final form April 3, 2013; Published online April 17, 2013
Bibliographic databases:
Document Type: Article
MSC: 58A30; 53C17; 58A15; 53C10
Language: English
Citation: Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens, “Geometry of Optimal Control for Control-Affine Systems”, SIGMA, 9 (2013), 034, 31 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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