Skip to main content
SpringerLink
Log in

Sub-Riemannian Optimization

  • Living reference work entry
  • First Online:
Book cover Encyclopedia of Systems and Control

  • 412 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

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 

Download references

Author information

Authors and Affiliations

  1. Harvard University, Cambridge, MA, USA

    Roger Brockett

Authors
  1. Roger Brockett
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

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

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag London

About this entry

Cite this entry

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

Download citation

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

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

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

Publish with us

Policies and ethics

Search

Navigation