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Encyclopedia of Systems and Control pp 1–6Cite as

Sub-Riemannian Optimization

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Abstract

Optimization problems arising in the control of some important types of physical systems lead naturally to problems in sub-Riemannian optimization. Here we provide context and background material on the relevant mathematics and discuss some specific problem areas where these ideas play a role.

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Notes

  1. 1.

    This work was supported in part by the US Army Research Office under grant DAAG 55 97 1 0114, DARPA under grant DAAH 04 96 1 0445

Bibliography

  • Baillieul J (1975) Some optimization problems in geometric control theory. PhD thesis, Harvard University

    Google Scholar 

  • Brockett R (1973a) Lie theory and control systems defined on spheres. SIAM J Appl Math 25:213–225

    Article  MATH  MathSciNet  Google Scholar 

  • Brockett R (1973b) Lie algebras and lie groups in control theory. In: Mayne DQ, Brockett RW (eds) Geometric methods in system theory. Reidel, Dordrecht, pp 43–82

    Chapter  Google Scholar 

  • Brockett R (1999) Explicitly solvable control problems with nonholonomic constraints. In: Proceedings of the 1999 CDC conference, Phoenix, pp 13–16

    Google Scholar 

  • Brockett R (2003) Pattern generation and the control of nonlinear systems. IEEE Trans Autom Control 48:1699–1712

    Article  MathSciNet  Google Scholar 

  • Gromov M (1996) Carnot-Carathéodory spaces seen from within. Sub-Riemannian geometry. Progress in mathematics, vol 144. Birkhäuser, Basel, pp 79–323

    Google Scholar 

  • Strichartz RS (1986) Sub-Riemannian geometry. J Diff Geom 24:221–263

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Harvard University, Cambridge, MA, USA

    Roger Brockett

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  1. Roger Brockett
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Correspondence to Roger Brockett .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2014 Springer-Verlag London

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Brockett, R. (2014). Sub-Riemannian Optimization. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_48-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_48-1

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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