Skip to main content
SpringerLink
Log in

Controllability for a class of nondiagonal hyperbolic distributed bilinear systems

  • Published:
Applied Mathematics and Optimization Submit manuscript

Abstract

This paper studies controllability of the abstract “hyperbolic” control systemü + Au + p(t)Bu = 0 whereA andB are (possibly) unbounded linear operators on an infinite dimensional Hilbert spaceH andp(t) is a real valued scalar control. The paper gives conditions for elements of the underlying state space to be accessible from prescribed initial data (u(0),57-1 Applications to wave equations are provided.

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. Ball JM, Slemrod M (1979) Nonharmonic Fourier series and the stabilization of distributed semi-linear control systems. Comm Pure Appl Math 33:555–587

    Google Scholar 

  2. Ball JM, Marsden JE, Slemrod M (1982) Controllability for distributed bilinear systems. SIAM J Control Optim 20:575–597

    Google Scholar 

  3. Brockett R (1972) System theory on group manifolds and coset spaces. SIAM J Control 10:265–284

    Google Scholar 

  4. Gohberg IC, Krein MG (1969) Introduction to the theory of linear nonself adjoint operators. Amer Math Soc Transl, vol 18. Amer Math Soc, Providence, RI

    Google Scholar 

  5. Hermes H (1974) On local and global controllability. SIAM J. Control 12:252–261

    Google Scholar 

  6. Hermes H (1979) Local controllability of observables in finite and infinite dimensional nonlinear control systems. Appl Math Optim 5:117–125

    Google Scholar 

  7. Jurdjevic V, Quinn J (1978) Controllability and stability. J Differential Eq 28:281–289

    Google Scholar 

  8. Kato T (1966) Perturbation theory for linear operators. Springer-Verlag, New York

    Google Scholar 

  9. Luenberger DG (1969) Optimization by vector space methods. John Wiley, New York

    Google Scholar 

  10. Riesz F, Nagy B Sz (1955) Functional analysis. F. Ungar, New York

    Google Scholar 

  11. Russell D (1967) Nonharmonic Fourier series in the control theory of distributed parameter systems. J Math Anal Appl 18:542–560

    Google Scholar 

  12. Russell D (1973) A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Studies Appl Math 52:189–211

    Google Scholar 

  13. Russell D (1978) Controllability and stabilizability theory for partial differential equations: Recent progress and open questions. SIAM Review 20:639–739

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 12181, Troy, NY, USA

    M. Slemrod

Authors
  1. M. Slemrod
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by D. Kinderlehrer

This research was supported in part by the Air Force office of Scientific Research, Air Force Systems Command, USAF, under Contract/Grant No. AFORS-81-0172. The United States Government if authorized to reproduce and distribute reprints for government purposes not withstanding any copyright herein.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Slemrod, M. Controllability for a class of nondiagonal hyperbolic distributed bilinear systems. Appl Math Optim 11, 57–76 (1984). https://doi.org/10.1007/BF01442170

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01442170

Keywords

Search

Navigation