Advertisement

Ein Kontroll-Approximationsproblem für die Schwingende Saite

  • Werner Krabs
Part of the International Series of Numerical Mathematics book series (ISNM, volume 30)

Abstract

In this paper the problem of controlling a vibrating string at the righthand side is considered where the left end is fixed. First the question of controllability is discussed, i.e. the question how to achieve, in a given fixed time, the complete standstill starting with an arbitrary initial state of vibration and controlling by continuous functions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. [1]
    Butkovskiy,A.G.: Theory of optimal control of distributed parameter systems. Elsevier Publ. Comp., New York-London-Amsterdam 1969Google Scholar
  2. [2]
    Butkovskiy, A.G.: The method of moments in the theory of optimal control systems with distributed parameters. Automat.Remote Control 24 (1963), 11o6–1113Google Scholar
  3. [3]
    Butkovskiy, A.G. and L.N.Poltayskii: The optimal control of a distributed oscillating system. Automat.Remote Control 26 (1965), 1835–1848MathSciNetGoogle Scholar
  4. [4]
    Köthe,G.: Topologische lineare Räume I,SpringerVerlag, Berlin-Heidelberg-New York 1966,2.Aufl.Google Scholar
  5. [5]
    Roxin,E.: Optimierungsprobleme mit der Wellen, gleichung.Preprint Nr.146 des Fachbereichs Mathematik der TH Darmstadt, Juli 1974Google Scholar
  6. [6]
    Russell, D.L.: On boundary-value controllability of linear symmetric hyperbolic systems. “Proceedings of the Conference on the Mathematical Theory of Control”,Univ.of Southern Calif.,Academic Press, New York 1967,pp. 312–321Google Scholar
  7. [7]
    Russell, D.L.: Nonharmonic Fourier series in the control of distributed parameter systems.J.Mathem. Anal.Appl. 18 (1967), 542–56ozbMATHCrossRefGoogle Scholar
  8. [8]
    Triebel,H.: Höhere Analysis.VEB Deutscher Verlag der Wissenschaften, Berlin 1972Google Scholar

Copyright information

© Springer Basel AG 1976

Authors and Affiliations

  • Werner Krabs
    • 1
  1. 1.Fachbereich Mathematik der TH Darmstadt61 DarmstadtGermany

Personalised recommendations