Skip to main content
SpringerLink
Log in

Characterizations of Hamiltonian control systems

  • I-Differential Geometric System Theory Structural Properties
  • Conference paper
  • First Online:
New Trends in Nonlinear Control Theory

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 122))

Abstract

Given a control system with an output, we give explicit conditions on the system which guarantee that it admits a Hamiltonian structure. The conditions are stated directly in terms of vector fields and observation functions defined by the system.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W.M. Boothby, “An Introduction to Differentiable Manifolds and Riemannian Geometry”, Academic Press, New York 1975.

    Google Scholar 

  2. R.W. Brockett, A. Rahimi, Lie algebras and linear differential equations, in “Ordinary Differential Equations”, ed. L. Weiss, Academic Press, New York 1972.

    Google Scholar 

  3. C.I. Byrnes, T.E. Duncan, A note on the topology of spaces of Hamiltonian transfer functions, in Lectures in Applied Mathematics, Vol.18, American Mathematical Society 1980.

    Google Scholar 

  4. P.E. Crouch, M. Irving, On finite Volterra series which admit Hamiltonian realizations, Math. Systems Theory 17 (1984), 293–318.

    Google Scholar 

  5. P.E. Crouch, Hamiltonian realizations of finite Volterra series, in “Geometric Theory of Nonlinear Control Systems”, eds. B. Jakubczyk, W. Respondek, K. Tchon, Technical University of Wroclaw 1985.

    Google Scholar 

  6. P.E. Crouch, A.J. Van der Schaft, “Variational Characterization of Hamiltonian Systems”, Lecture Notes in Control and Information Sciences, Springer 1987.

    Google Scholar 

  7. B. Jakubczyk, Hamiltonian Realizations of Nonlinear Systems, Proc. MTNS-85, C. Byrnes, A. Lindquist eds. North-Holland 1986.

    Google Scholar 

  8. B. Jakubczyk, Poisson structures and relations on vector fields and their Hamiltonians, Bull. Pol. Acad. Sci. Ser. Math. 34, (1986), 713–721.

    Google Scholar 

  9. B. Jakubczyk, Existence of Hamiltonian realizations of nonlinear causal operators, Bull. Pol. Acad. Sci. Ser. Math 34. (1986), 737–747.

    Google Scholar 

  10. A.J. Van der Schaft, “System Theoretic Descriptions of Physical Systems”, CWI Tract No. 3, Amsterdam 1984.

    Google Scholar 

  11. A.J. Van der Schaft, P.E. Crouch, Hamiltonian and self-adjoint control systems, Systems and Control Letters 8 (1987), 289–295.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950, Warsaw, Poland

    B. Jakubczyk

Authors
  1. B. Jakubczyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. Descusse Michel Fliess A. Isidori D. Leborgne

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Jakubczyk, B. (1989). Characterizations of Hamiltonian control systems. In: Descusse, J., Fliess, M., Isidori, A., Leborgne, D. (eds) New Trends in Nonlinear Control Theory. Lecture Notes in Control and Information Sciences, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043012

Download citation

  • DOI: https://doi.org/10.1007/BFb0043012

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51075-8

  • Online ISBN: 978-3-540-46143-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation