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Complete Controllability of a Delayed Semilinear Stochastic Control System

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Mathematical Analysis and its Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 143))

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Abstract

In this paper, complete controllability of a delayed semilinear stochastic system is considered under some basic and readily verified conditions. A fixed-point approach is employed for achieving the required result. At the end, an example is given to show the effectiveness of the result.

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References

  1. Kalman, R.E.: Controllability of linear systems. Contribut. Differ. Equ. 1, 190–213 (1963)

    MathSciNet  Google Scholar 

  2. Curtain, R.F., Zwart, H.: An introduction to infinite-dimensional linear systems theory. Texts in Applied Mathematics, p. 21. Springer, New York (1995)

    Book  MATH  Google Scholar 

  3. Barnett, S.: Introduction to Mathematical Control Theory. Clarendon Press, Oxford (1975)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Klamka, J.: Stochastic controllability of linear systems with delay in control. Bullet. Polish Acad. Sci. 55, 23–29 (2007)

    MATH  Google Scholar 

  6. Klamka, J., Socha, L.: Some remarks about stochastic controllability. IEEE Trans. Automatic Control AC 22(5), 880–881 (1977)

    Google Scholar 

  7. Klamka, J., Socha, L.: Some remarks about stochastic controllability for delayed linear systems. Internat. J. Control 32(3), 561–566 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mahmudov, N.I.: Controllability of linear stochastic systems. IEEE Trans. Automat. Control 46(5), 724–731 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Mahmudov, N.I.: Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. SIAM J. Control Optim. 42(5), 1604–1622 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mahmudov, N.I., Zorlu, S.: Controllability of nonlinear stochastic systems. J. Control 76, 95–104 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mahmudov, N.I.: On controllability of semilinear stochastic systems in Hilbert spaces. IMA J. Math. Control Inform. 19(4), 363–376 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mahmudov, N.I.: Controllability of linear stochastic systems in Hilbert spaces. J. Math. Anal. Appl. 259(1), 64–82 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Mahmudov, N.I., Semi, N.: Approximate controllability of semilinear control systems in Hilbert spaces. TWMS J. App. Eng. Math. 2(1), 67–74 (2012)

    Google Scholar 

  14. Mahmudov, N.I., Denker, A.: On controllability of linear stochastic systems. Internat. J. Control 73(2), 144–151 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Shen, L., Sun, J.: Relative controllability of stochastic nonlinear systems with delay in control. Nonlinear Anal. Real World Appl. 13(6), 2880–2887 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Sakthivel, R., Kim, J.-H., Mahmudov, N.I.: On controllability of nonlinear stochastic systems. Rep. Math. Phys. 58(3), 433–443 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Da Prato, G., Zabczyk, J.: Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (1992)

    Book  MATH  Google Scholar 

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Acknowledgments

The authors express their sincere gratitude to the reviewers for their valuable suggestions for improving the paper. This research is supported by the Ministry of Human Resource and Development (MHRD) in the form of fellowship to the first author.

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Correspondence to Urvashi Arora .

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Arora, U., Sukavanam, N. (2015). Complete Controllability of a Delayed Semilinear Stochastic Control System. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_43

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