Skip to main content
SpringerLink
Log in

Numerical solution of minimum norm problems of distributed control of vibrations

  • Published:
Applied Mathematics & Optimization Aims and scope Submit manuscript

Abstract

This paper is concerned with the distributed control of a vibration process that can be described by a differential equation for a Hilbert-spacevalued functiony: [0, ∞) → H. The control functions on the right-hand side of this equation are taken fromL∞([0, ∞),H) equipped with the essential supremum norm. To be solved is the problem of time-minimal null-controllability by norm-bounded controls. This problem is essentially reduced to solving the problem of minimum norm control on a given time interval. This is solved via its dual problem which is approximately solved by truncation and discretization. Numerical results are presented for a vibrating string and a vibrating beam.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fattorini HO (1977) The time optimal problem for distributed control of systems governed by the wave equation. In: Aziz AK, Wingate JW, Balas MJ (eds) Control Theory of Systems Governed by Partial Differential Equations. Academic Press, New York

    Google Scholar 

  2. Krabs W (1981) Time minimal controllability in view of optimization. In: Auslender A, Oettli W, Stoer J (eds) Optimization and Optimal Control. Lecture Notes in Control and Information Sciences, vol 30. Springer-Verlag, Berlin, pp 211–277

    Google Scholar 

  3. Krabs W (1982) Convex optimization and approximation. In: Korte B (ed) Modern Applied Mathematics: Optimization and Operations Research. North-Holland, Amsterdam, pp 327–357

    Google Scholar 

  4. Krabs W (1985) On time-minimal distributed control of vibrating systems governed by an abstract wave equation. Appl Math Optim 13:137–149

    Article  MathSciNet  MATH  Google Scholar 

  5. Krabs W (1989) On time-minimal distributed control of vibrations. Appl Math Optim 19:65–73

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technischen Hochschule Darmstadt, Schlossgartenstrasse 7, 6100, Darmstadt, West Germany

    W. Krabs & Zheng Yan

Authors
  1. W. Krabs
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krabs, W., Yan, Z. Numerical solution of minimum norm problems of distributed control of vibrations. Appl Math Optim 21, 243–264 (1990). https://doi.org/10.1007/BF01445165

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01445165

Keywords

Search

Navigation