Skip to main content

Controllability of nonlinear impulsive Ito type stochastic systems Cover

.blurhash-client-img { display: none !important; }

Controllability of nonlinear impulsive Ito type stochastic systems

International Journal of Applied Mathematics and Computer Science

Volume 19 (2009): Issue 4 (December 2009)

By: Rathinasamy Sakthivel

Open Access

|Dec 2009

Abstract

In this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.

References

Alotaibi, S., Sen, M., Goodwine, B. and Yang, K. T. (2004). Controllability of cross-flow heat exchangers, International Journal of Heat and Mass Transfer 47(5): 913-924.10.1016/j.ijheatmasstransfer.2003.08.021
Search in Google Scholar
Balachandran, K. and Sakthivel, R. (2001). Controllability of integrodifferential systems in Banach spaces, Applied Mathematics and Computation 118(1): 63-71.10.1016/S0096-3003(00)00040-0
Search in Google Scholar
Balasubramaniam, P. and Dauer, J. P. (2003). Controllability of semilinear stochastic evolution equations with time delays, Publicationes Mathematicae Debrecen 63(3): 279-291.
Search in Google Scholar
Bashirov, A. E. and Mahmudov, N. I. (1999). On concepts of controllability for deterministic and stochastic systems, SIAM Journal on Control and Optimization 37(6): 1808-1821.10.1137/S036301299732184X
Search in Google Scholar
Keck, D. N. and McKibben, M. A. (2006). Abstract semilinear stochastic Ito Volterra integrodifferential equations, Journal of Applied Mathematics and Stochastic Analysis 20(2): 1-22.10.1155/JAMSA/2006/45253
Search in Google Scholar
Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer, Dordrecht.
Search in Google Scholar
Klamka, J. (2000). Schauders fixed-point theorem in nonlinear controllability problems, Control and Cybernetics 29(1): 153-165.
Search in Google Scholar
Klamka, J. (2007a). Stochastic controllability of linear systems with delay in control, Bulletin of the Polish Academy of Sciences: Technical Sciences 55(1): 23-29.
Search in Google Scholar
Klamka, J. (2007b). Stochastic controllability of linear systems with state delays, International Journal of Applied Mathematics and Computer Science 17(1): 5-13.10.2478/v10006-007-0001-8
Search in Google Scholar
Klamka, J. and Socha, L. (1977). Some remarks about stochastic controllability, IEEE Transactions on Automatic Control 22(5): 880-881.10.1109/TAC.1977.1101615
Search in Google Scholar
Klamka, J. and Socha, L. (1980). Some remarks about stochastic controllability for delayed linear systems, International Journal of Control 32(3): 561-566.10.1080/00207178008922872
Search in Google Scholar
Liu, B., Liu, X. Z. and Liao, X. X. (2007). Existence and uniqueness and stability of solutions for stochastic impulsive systems, Journal of Systems Science and Complexity 20(1): 149-158.10.1007/s11424-007-9013-6
Search in Google Scholar
Mahmudov, N. I. (2001). Controllability of linear stochastic systems, IEEE Transactions on Automatic Control 46(1): 724-731.10.1109/9.920790
Search in Google Scholar
Mahmudov, N. I. and Zorlu, S. (2003). Controllability of nonlinear stochastic systems, International Journal of Control 76(2): 95-104.10.1080/0020717031000065648
Search in Google Scholar
Mahmudov, N. I. and Zorlu, S. (2005). Controllability of semilinear stochastic systems, International Journal of Control 78(13): 997-1004.10.1080/00207170500207180
Search in Google Scholar
Mao, X. (1997). Stochastic Differential Equations and Applications, Elis Horwood, Chichester.
Search in Google Scholar
Murge, M. G. and Pachpatte, B. G. (1986a). Explosion and asymptotic behavior of nonlinear Ito type stochastic integro-differential equations, Kodai Mathematical Journal 9(1): 1-18.10.2996/kmj/1138037145
Search in Google Scholar
Murge, M. G. and Pachpatte, B. G. (1986b). On generalized Ito type stochastic integral equation, Yokohama Mathematical Journal 34(1-2): 23-33.
Search in Google Scholar
Rao, A. N. V. and Tsokos, C. P. (1995). Stability of impulsive stochastic differential systems, Dynamical Systems and Applications 4(4): 317-327.
Search in Google Scholar
Respondek, J. (2005). Numerical approach to the non-linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems, International Journal of Control 78(13): 1017-1030.10.1080/00207170500197605
Search in Google Scholar
Respondek, J. S. (2007). Numerical analysis of controllability of diffusive-convective system with limited manipulating variables, International Communications in Heat and Mass Transfer 34(8): 934-944.10.1016/j.icheatmasstransfer.2007.04.005
Search in Google Scholar
Respondek, J. S. (2008). Approximate controllability of infinite dimensional systems of the n-th order, International Journal of Applied Mathematics and Computer Science 18(2): 199-212.10.2478/v10006-008-0018-7
Search in Google Scholar
Sakthivel, R., Kim, J. H. and Mahmudov, N. I. (2006). On controllability of nonlinear stochastic systems, Reports on Mathematical Physics 58(3): 433-443.10.1016/S0034-4877(06)80963-8
Search in Google Scholar
Samoilenko, A. M. and Perestyuk, N. A. (1995). Impulsive Differential Equations, World Scientific, Singapore.10.1142/2892
Search in Google Scholar
Sunahara, Y., Kabeuchi, T., Asad, Y., Aihara, S. and Kishino, K. (1974). On stochastic controllability for nonlinear systems, IEEE Transactions on Automatic Control 19(1): 49-54.10.1109/TAC.1974.1100464
Search in Google Scholar
Yang, Z., Xu, D. and Xiang, L. (2006). Exponential p-stability of impulsive stochastic differential equations with delays, Physics Letters A 359(2): 129-137.10.1016/j.physleta.2006.05.090
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/v10006-009-0046-y | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X

Journal RSS Feed

Language: English

Page range: 589 - 595

Published on: Dec 31, 2009

Published by: University of Zielona Góra

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

complete controllability,

resolvent matrix,

impulsive Ito type stochastic equations,

Brownian motion

Related subjects:

Applied mathematics

© 2009 Rathinasamy Sakthivel, published by University of Zielona Góra
This work is licensed under the Creative Commons License.

Volume 19 (2009): Issue 4 (December 2009)