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CONTROLLABILITY OF STOCHASTIC FUNCTIONAL INTEGRODIFFERENTIAL EVOLUTION SYSTEMS

  • Kokila, J. (Department of Mathematics, Bharathiar University) ;
  • Balachandran, K. (Department of Mathematics, Bharathiar University)
  • Received : 2010.07.30
  • Accepted : 2010.10.12
  • Published : 2011.05.30

Abstract

In this paper, we prove the existence and uniqueness of mild solution for stochastic functional integrodifferential evolution equations and derive sufficient conditions for the controllability results. As an illustration we consider the controllability for a system governed by a random motion of a string.

Keywords

References

  1. K.J.Astrom, Introduction to Stochastic Control Theory, Academic Press, New York, 1970.
  2. K.Balachandran, S.Karthikeyan, Controllability of stochastic integrodifferential systems, Int. J. Control. 80(2007), 486-491. https://doi.org/10.1080/00207170601115977
  3. K.Balachandran, J.H.Kim, S.Karthikeyan, Controllability of semilinear stochastic integrod- ifferential equations, Kybernetika, 43(2007), 31-44.
  4. K.Balachandran, J.H.Kim, S.Karthikeyan, Complete controllability of stochastic integrodifferential systems, Dyn. Syst. Appl. 17(2008), 43-52.
  5. P.Balasubramaniam, Controllability of quasilinear stochastic evolution equations in Hilbert spaces, J. Appl. Math. Stoch. Anal. 14(2001), 151-159. https://doi.org/10.1155/S1048953301000119
  6. P.Balasubramaniam, J.P.Dauer, Controllability of semilinear stochastic evolution equations in Hilbert spaces, J. Appl. Math. Stoch. Anal. 14(2001), 329-339. https://doi.org/10.1155/S1048953301000296
  7. P.Balasubramaniam, J.Y.Park, P.Muthukumar, Approximate controllability of neutral stochastic functional differential systems with infinite delay, Stoch. Anal. Appl. 28(2010), 389-400. https://doi.org/10.1080/07362990802405695
  8. G.Da Prato, J.Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.
  9. G.Da Prato, J.Zabczyk, Ergodicity for infinite Dimensional Systems, Cambridge University Press, Cambridge, 1996.
  10. J.P. Dauer, N.I. Mahmudov, Controllability of stochastic semilinear functional differential equations in Hilbert spaces, J. Math. Anal. Appl. 290(2004), 373-394. https://doi.org/10.1016/j.jmaa.2003.09.069
  11. A.Jentzen, P.E.Kloeden, A unified existence and uniqueness theorem for stochasic evolution equations, Bull. Aust. Math. Soc. 81(2010), 33-46. https://doi.org/10.1017/S0004972709000677
  12. R.MacCamy, An integrodifferential equation with applications in heat flow, Q. Appl. Math. 35(1977/78), 1-99.
  13. N.I.Mahmudov, Controllability of semilinear stochastic systems in Hilbert spaces, J. Math. Anal. Appl. 288(2003), 197-211. https://doi.org/10.1016/S0022-247X(03)00592-4
  14. C.Prµevot, M.Rockner, A Concise Course on Stochastic Partial Differential Equations, Springer, Berlin, 2007.
  15. G.R.Sell, Y.You, Dynamics of Evolutionary Equations, Springer, New York, 2002.
  16. R.Subalakshmi, K.Balachandran, J.Y.Park, Controllability of semilinear stochastic functional integrodifferential systems in Hilbert spaces, Nonlinear Analysis: Hybrid Systems, 3(2009), 39-50. https://doi.org/10.1016/j.nahs.2008.10.004
  17. W.M.Wonham, Random differential equations in control theory, Probab. Methods Appl. Math. 2(1970), 131-212.
  18. J.Zabczyk, Controllability of Stochastic Linear Systems, Syst. Control Lett. 1(1982), 25- 31.