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
Kalman, R.E.: Controllability of linear systems. Contribut. Differ. Equ. 1, 190–213 (1963)
Curtain, R.F., Zwart, H.: An introduction to infinite-dimensional linear systems theory. Texts in Applied Mathematics, p. 21. Springer, New York (1995)
Barnett, S.: Introduction to Mathematical Control Theory. Clarendon Press, Oxford (1975)
Klamka, J.: Stochastic controllability of linear systems with state delays. Int. J. Appl. Math. Comput. Sci. 17(1), 5–13 (2007)
Klamka, J.: Stochastic controllability of linear systems with delay in control. Bullet. Polish Acad. Sci. 55, 23–29 (2007)
Klamka, J., Socha, L.: Some remarks about stochastic controllability. IEEE Trans. Automatic Control AC 22(5), 880–881 (1977)
Klamka, J., Socha, L.: Some remarks about stochastic controllability for delayed linear systems. Internat. J. Control 32(3), 561–566 (1980)
Mahmudov, N.I.: Controllability of linear stochastic systems. IEEE Trans. Automat. Control 46(5), 724–731 (2001)
Mahmudov, N.I.: Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. SIAM J. Control Optim. 42(5), 1604–1622 (2003)
Mahmudov, N.I., Zorlu, S.: Controllability of nonlinear stochastic systems. J. Control 76, 95–104 (2003)
Mahmudov, N.I.: On controllability of semilinear stochastic systems in Hilbert spaces. IMA J. Math. Control Inform. 19(4), 363–376 (2002)
Mahmudov, N.I.: Controllability of linear stochastic systems in Hilbert spaces. J. Math. Anal. Appl. 259(1), 64–82 (2001)
Mahmudov, N.I., Semi, N.: Approximate controllability of semilinear control systems in Hilbert spaces. TWMS J. App. Eng. Math. 2(1), 67–74 (2012)
Mahmudov, N.I., Denker, A.: On controllability of linear stochastic systems. Internat. J. Control 73(2), 144–151 (2000)
Shen, L., Sun, J.: Relative controllability of stochastic nonlinear systems with delay in control. Nonlinear Anal. Real World Appl. 13(6), 2880–2887 (2012)
Sakthivel, R., Kim, J.-H., Mahmudov, N.I.: On controllability of nonlinear stochastic systems. Rep. Math. Phys. 58(3), 433–443 (2006)
Da Prato, G., Zabczyk, J.: Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (1992)
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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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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DOI: https://doi.org/10.1007/978-81-322-2485-3_43
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