Skip to main content
SpringerLink
Log in

Approximate Controllability for Integrodifferential Equations with Multiple Delays

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

This paper considers the approximate controllability for a class of control systems governed by semilinear delay integrodifferential equations with multiple delays. Sufficient conditions for approximate controllability are established by using the Schauder fixed-point theorem. The results obtained improve some analogous existing results. Several examples are provided to illustrate the application of the approximate controllability result.

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. Balachandran, K., Dauer, J.P.: Controllability of nonlinear systems in Banach spaces: a survey. J. Optim. Theory Appl. 115, 7–28 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Klamka, J.: Constrained controllability of semilinear systems. Nonlinear Anal. 47, 2939–2949 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Klamka, J.: Constrained exact controllability of semilinear systems. Syst. Control Lett. 47, 139–147 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Triggiani, R.: A note on the lack of exact controllability for mild solutions in Banach spaces. SIAM J. Control Optim. 15, 407–411 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  5. Choi, J.R., Kwun, Y.C., Sung, Y.K.: Approximate controllability for nonlinear integrodifferential equations. J. Korea Soc. Math. Educ. 2, 173–181 (1995)

    MathSciNet  Google Scholar 

  6. Dauer, J.P., Mahmudov, N.I.: Controllability of some nonlinear systems in Hilbert spaces. J. Math. Anal. Appl. 123, 319–329 (2004)

    MathSciNet  Google Scholar 

  7. Fabre, C., Puel, J.P., Zuazua, E.: Approximate controllability of semilinear heat equation. Proc. R. Soc. Edinb. Sect. A Math. 125, 31–61 (1995)

    MATH  MathSciNet  Google Scholar 

  8. Fernandez, L.A., Zuazua E.: Approximate controllability for semilinear heat equation involving gradient terms. J. Optim. Theory Appl. 101, 307–328 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Li, X., Yong, J.: Optimal Control Theory for Infinite Dimensional Systems. Birkhäuser, Basel (1994)

    MATH  Google Scholar 

  10. Mahmudov, N.I.: Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. SIAM J. Control Optim. 42, 1604–1622 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Naito, K.: Controllability of semilinear system dominated the linear part. SIAM J. Control Optim. 25, 715–722 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  12. Wang, L.: Approximate controllability and approximate null controllability of semilinear systems. Commun. Pure Appl. Anal. 5, 953–962 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Zhou, H.X.: Approximate controllability for a class of semilinear abstract equations. SIAM J. Control Optim. 21, 551–565 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  14. Jeong, J.M., Roh, H.H.: Approximate controllability for semilinear retarded systems. J. Math. Anal. Appl. 321, 961–975 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  15. Jeong, J.M., Kwun, Y.C., Park, J.Y.: Approximate controllability for semilinear retarded functional differential equations. J. Dyn. Control Syst. 5, 329–346 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  16. Naito, K., Park, J.Y.: Approximate controllability for trajectories of a delay Volterra control system. J. Optim. Theory Appl. 61, 271–279 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ryu, J.W., Park, J.Y., Kwun, Y.C.: Approximate controllability of delay Volterra control system. Bull. Korean Math. Soc. 30, 277–284 (1993)

    MATH  MathSciNet  Google Scholar 

  18. Dauer, J.P., Mahmudov, N.I.: Approximate controllability of semilinear functional equations in Hilbert spaces. J. Math. Anal. Appl. 273, 310–327 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Wang, L.: Approximate controllability of delayed semilinear control systems. J. Appl. Math. Stoch. Anal. 11, 67–76 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Central Missouri, Warrensburg, MO, 64093, USA

    L. W. Wang

Authors
  1. L. W. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. W. Wang.

Additional information

Communicated by Q.C. Zhao.

The author wishes to thank the two anonymous referees for their valuable suggestions and comments which have resulted in a great improvement of the paper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, L.W. Approximate Controllability for Integrodifferential Equations with Multiple Delays. J Optim Theory Appl 143, 185–206 (2009). https://doi.org/10.1007/s10957-009-9545-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-009-9545-0

Keywords

Search

Navigation