Skip to main content

A Note on the Reachable Sets of Control Systems

  • Chapter

Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 7))

Abstract

Let M be a finite dimensional differential manifold and let (∑u) be a timeindependent control system on M, that is a family of differential equations on M

$$(\Sigma ) \dot{x} = f(x,u)$$

parametrized by a set u⊆L 1loc (R,R m) of controls maps. u is called the set of admissible controls.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.M. Bianchini - G. Stefani “Multivalued fields and control systems withunbounded controls” Ricerche di Automatica 12 (1981) pp. 33–49.

    Google Scholar 

  2. A. Haefliger “Varietees feuilletees” Annali della Scuola Norm. Sup. PisavolXVI (1962) pp. 367–397

    Google Scholar 

  3. C. Lobry - “Sur l‘ensemble des points atteignables par les solutions d’uneequation differentielle multivoque” Plub. Math. Bordeaux Annee I, Fasc. 5(1973) pp. 43–60.

    Google Scholar 

  4. N. Kalouptsidis - D.L. Elliot “Accessibility properties of smooth nonlinearcontrol system” AMES Research Centre 1976, Martin & Hermann ed., Math.Sci. Press, Brookline, (1977) pp. 439–446.

    Google Scholar 

  5. P. Stefan - “Accessible sets, orbits and foliations with singularities” Proc.London Math. Soc. 29 (1974) pp. 699–713.

    Article  Google Scholar 

  6. H.J. Sussmann “Orbits of families of vector fields and integrability of systemswith singularities” Trans. Amer. Math. Soc. 180 (1973) pp. 171–188.

    Article  Google Scholar 

  7. H.J. Sussmann - V. Jurdjevic “Controllability of nonlinear systems” J.Diff. Eq. 12 (1972) pp. 95–116.

    Article  Google Scholar 

  8. E. Sontag - H.J. Sussmann “Remarks on continuous feedback” CDC1980 pp. 916-921Rosa Maria Bianchini Gianna StefaniDipart. di Matematica U.Dini Dipart. di Matematica e Appl.50134 Firenze, Italy 80100 Napoli, Italy

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Bianchini, R.M., Stefani, G. (1991). A Note on the Reachable Sets of Control Systems. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0439-8_13

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6760-7

  • Online ISBN: 978-1-4612-0439-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics