Skip to main content
SpringerLink
Log in

S-Controllability of a partially observed semilinear integrodifferential stochastic control system

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

In this article, some sufficient conditions are given for the S-controllability of a partially observed semilinear integrodifferential stochastic control system. Here, we established the controllability result using the separation principle approach in which the given semilinear stochastic control system is splitted into two control systems, namely one is semilinear deterministic control system and another is linear stochastic control system. An example is given to illustrate the 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. Tsokos CP, Padgett WJ (1974) Random integral equations with application to life sciences and engineering. Academic Press, New York

    MATH  Google Scholar 

  2. Bellman R, Jacquez J, Kalaba R (1960) Some mathematical aspect of chemotherapy. I: one-organ models. Bull Math Biophys 22:181–198

    Article  MathSciNet  Google Scholar 

  3. Kalman RE, Ho TC, Narendra KS (1963) Controllablity of linear dynamical systems. Contrib Differ Equ 1:190–213

    Google Scholar 

  4. Balachandran K, Dauer JP (2002) Controllability of nonlinear systems in Banach spaces: a survey. J Optim Theory Appl 115(1):7–28

    Article  MathSciNet  MATH  Google Scholar 

  5. Naito K (1987) Controllability of semilinear control systems dominated by the linear part. SIAM J Control Optim 25:715–722

    Article  MathSciNet  MATH  Google Scholar 

  6. Klamka J (2008) Constrained controllability of semilinear systems with delayed controls. Bull Pol Acad Sci Tech Sci 56(4):333–337

    Google Scholar 

  7. Kumar M, Sukavanam N (2015) Exact controllability of semilinear thermoelastic systems with monotone nonlinearity. Numer Funct Anal Optim 36:1163–1177

    Article  MathSciNet  MATH  Google Scholar 

  8. Kumar M, Kumar S (2016) Approximate controllability of second order semilinear control systems with bounded delay. Nonlinear Stud 23(2):323–331

    MathSciNet  MATH  Google Scholar 

  9. Sunahara Y, Kabeuchi T, Asada Y, Aihara S, Kishino K (1974) On stochastic controllability for nonlinear systems. IEEE Trans Autom Control 19:49–54

    Article  MathSciNet  MATH  Google Scholar 

  10. Sunahara Y, Aihara S, Kishino K (1975) On the stochastic controllability and observability for nonlinear systems. Int J Control 22:65–82

    Article  MATH  Google Scholar 

  11. Klamka J, Socha L (1977) Some remarks about stochastic controllability. IEEE Trans Autom Control 22:880–881

    Article  MathSciNet  MATH  Google Scholar 

  12. Bashirov AE (1996) On weakening of the controllability concepts. In: Proceedings of the 35th IEEE conference on decision and control, Kobe, Japan, vol 1, pp 640–645

  13. Bashirov AE, Kerimov KR (1997) On controllability conception for stochastic systems. SIAM J Control Optim 35:384–398

    Article  MathSciNet  MATH  Google Scholar 

  14. Bashirov AE, Mahmudov NI (1999) Controllability of linear deterministic and stochastic systems. In: 38th IEEE conference on decision and control, vol 4, Phoenix, AZ, USA, pp 3196–3202

  15. Bashirov AE, Mahmudov NI (1999) On concepts of controllability for deterministic and stochastic systems. SIAM J Control Optim 37(6):1808–1821

    Article  MathSciNet  MATH  Google Scholar 

  16. Mahmudov NI (2001) Controllability of linear stochastic systems in Hilbert spaces. J Math Anal Appl 259(1):64–82

    Article  MathSciNet  MATH  Google Scholar 

  17. Mahmudov NI, Zorlu S (2005) Controllability of semilinear stochastic systems. Int J Control 78:997–1004

    Article  MathSciNet  MATH  Google Scholar 

  18. Balachandran K, Karthikeyan S (2007) Controllability of stochastic integrodifferential systems. Int J Control 80:486–491

    Article  MathSciNet  MATH  Google Scholar 

  19. Balachandran K, Kim JH, Karthikeyan S (2007) Controllability of semilinear stochastic integrodifferential systems. Kybernetika 43:31–44

    MathSciNet  MATH  Google Scholar 

  20. Subalakshmi R, Balachandran K, Park JY (2009) Controllability of semilinear stochastic functional integrodifferential systems in Hilbert spaces. Nonlinear Anal Hybrid Syst 3:39–50

    Article  MathSciNet  MATH  Google Scholar 

  21. Klamka J (2007) Stochastic controllability of linear systems with delay in control. Bull Pol Acad Sci Tech Sci 55(1):23–29

    MATH  Google Scholar 

  22. Klamka J (2007) Stochastic controllability of linear systems with state delays. Int J Appl Math Comput Sci 17(1):5–13

    Article  MathSciNet  MATH  Google Scholar 

  23. Klamka J (2008) Stochastic controllability and minimum energy control of systems with multiple delays in control. Appl Math Comput 206(2):704–715

    MathSciNet  MATH  Google Scholar 

  24. Klamka J (2008) Stochastic controllability of systems with variable delay in control. Bull Pol Acad Sci Tech Sci 56(3):279–284

    Google Scholar 

  25. Klamka J (2009) Stochastic controllability of systems with multiple delays in control. Int J Appl Math Comput Sci 19(1):39–47

    Article  MathSciNet  MATH  Google Scholar 

  26. Sakthivel R, Nieto JJ, Mahmudov NI (2010) Approximate controllability of nonlinear deterministic and stochastic systems with unbounded delay. Taiwan J Math 14:1777–1797

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Editor-in-Chief and the anonymous referees for their suggestions which helped to improve the quality of the presentation.

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttrakhand, 247667, India

    Mohit Kumar

  2. Department of Mathematics, Ch. Charan Singh University, Meerut, Uttar Pradesh, 250004, India

    Sandeep Kumar

Authors
  1. Mohit Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sandeep Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohit Kumar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, M., Kumar, S. S-Controllability of a partially observed semilinear integrodifferential stochastic control system. Int. J. Dynam. Control 6, 406–412 (2018). https://doi.org/10.1007/s40435-016-0279-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-016-0279-1

Keywords

Mathematics Subject Classification

Search

Navigation