About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Balachandran, Krishnan ; Karthikeyan, S. ; Kim, J.-H.
Controllability of semilinear stochastic integrodifferential systems. (English). Kybernetika, vol. 43 (2007), issue 1, pp. 31-44
MSC: 60H10, 93B05, 93C23, 93E03, 93E20 | MR 2343329 | Zbl 1137.93010
Keywords:
controllability; approximate controllability; stochastic integrodifferential system; Picard iteration
Summary:
In this paper we study the approximate and complete controllability of stochastic integrodifferential system in finite dimensional spaces. Sufficient conditions are established for each of these types of controllability. The results are obtained by using the Picard iteration technique.
References:
[1] Balachandran K., Dauer J.: Controllability of nonlinear systems via fixed point theorems. J. Optim. Theory Appl. 53 (1987), 345–352 DOI 10.1007/BF00938943 | MR 0891093 | Zbl 0596.93010
[2] Dauer J., Balachandran K.: Sample controllability of general nonlinear stochastic systems. Libertas Math. 17 (1997), 143–153 MR 1485673 | Zbl 0892.93010
[3] Dobov M. A., Mordukhovich B. S.: Theory of controllability of linear stochastic systems. Differential Equations 14 (1978), 1609–1612
[4] Enrhardt M., Kliemann W.: Controllability of stochastic linear systems. Systems Control Lett. 2 (1982), 45–153
[5] Klamka J.: Schauder’s fixed point theorem in nonlinear controllability problems. Control Cybernet. 29 (2000), 153–165 MR 1775163 | Zbl 1011.93001
[6] Klamka J., Socha L.: Some remarks about stochastic controllability. IEEE Trans. Automat. Control 22 (1977), 880–881 DOI 10.1109/TAC.1977.1101615 | MR 0456887 | Zbl 0363.93048
[7] Lipster R. S., Shiryaev A. N.: Statistics of Random Processes. Springer, New York 1977
[8] Mahmudov N. I., Denker A.: On controllability of linear stochastic systems. Internat. J. Control 73 (2000), 144–151 DOI 10.1080/002071700219849 | MR 1738365 | Zbl 1031.93033
[9] Mahmudov N. I.: Controllability of linear stochastic systems. IEEE Trans. Automat. Control 46 (2001), 724–731 DOI 10.1109/9.920790 | MR 1833025 | Zbl 1031.93034
[10] Mahmudov N. I.: On controllability of semilinear stochastic systems in Hilbert spaces. IMA J. Math. Control Inform. 19 (2002), 363–376 DOI 10.1093/imamci/19.4.363 | MR 1948289 | Zbl 1138.93313
[11] Mahmudov N. I.: Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. SIAM J. Control Optim. 42 (2004), 1604–1622 DOI 10.1137/S0363012901391688 | MR 2046377 | Zbl 1084.93006
[12] Mahmudov N. I., Zorlu S.: Controllability of nonlinear stochastic systems. Internat. J. Control 76 (2003), 95–104 DOI 10.1080/0020717031000065648 | MR 1965846 | Zbl 1111.93301
[13] Mahmudov N. I., Zorlu S.: Controllability of semilinear stochastic systems. Internat. J. Control 78 (2005), 997–1004 DOI 10.1080/00207170500207180 | MR 2164204 | Zbl 1097.93034
[14] Sunahara Y., Kabeuchi T., Asada, S., Kishino K.: On stochastic controllability for nonlinear systems. IEEE Trans. Automat. Control 19 (1974), 49–54 DOI 10.1109/TAC.1974.1100464 | MR 0359965
[15] Zabczyk J.: Controllability of stochastic linear systems. Systems Control Lett. 1 (1987), 25–31 DOI 10.1016/S0167-6911(81)80008-4 | MR 0667324
Partner of
EuDML logo