Abstract
In this paper, complete controllability for nonlinear stochastic systems is studied. First this paper addresses the problem of complete controllability of nonlinear stochastic systems with standard Brownian motion. Then this result is extended to establish complete controllability criterion for stochastic systems with fractional Brownian motion. A fixed point approach is employed for achieving the required result. The solutions are given by a variation of constants formula which allows us to study the complete controllability for nonlinear stochastic systems. In this paper, we prove the complete controllability of nonlinear stochastic system under the natural assumption that the associated linear control system is completely controllable. Finally, an illustrative example is provided to show the usefulness of the proposed technique.
| Original language | English |
|---|---|
| Pages (from-to) | 433-443 |
| Number of pages | 11 |
| Journal | Reports on Mathematical Physics |
| Volume | 58 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2006 Dec 1 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
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On controllability of nonlinear stochastic systems. / Sakthivel, R.; Kim, J. H.; Mahmudov, N. I.
In: Reports on Mathematical Physics, Vol. 58, No. 3, 01.12.2006, p. 433-443.Research output: Contribution to journal › Article
TY - JOUR
T1 - On controllability of nonlinear stochastic systems
AU - Sakthivel, R.
AU - Kim, J. H.
AU - Mahmudov, N. I.
PY - 2006/12/1
Y1 - 2006/12/1
N2 - In this paper, complete controllability for nonlinear stochastic systems is studied. First this paper addresses the problem of complete controllability of nonlinear stochastic systems with standard Brownian motion. Then this result is extended to establish complete controllability criterion for stochastic systems with fractional Brownian motion. A fixed point approach is employed for achieving the required result. The solutions are given by a variation of constants formula which allows us to study the complete controllability for nonlinear stochastic systems. In this paper, we prove the complete controllability of nonlinear stochastic system under the natural assumption that the associated linear control system is completely controllable. Finally, an illustrative example is provided to show the usefulness of the proposed technique.
AB - In this paper, complete controllability for nonlinear stochastic systems is studied. First this paper addresses the problem of complete controllability of nonlinear stochastic systems with standard Brownian motion. Then this result is extended to establish complete controllability criterion for stochastic systems with fractional Brownian motion. A fixed point approach is employed for achieving the required result. The solutions are given by a variation of constants formula which allows us to study the complete controllability for nonlinear stochastic systems. In this paper, we prove the complete controllability of nonlinear stochastic system under the natural assumption that the associated linear control system is completely controllable. Finally, an illustrative example is provided to show the usefulness of the proposed technique.
UR - http://www.scopus.com/inward/record.url?scp=34548312475&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34548312475&partnerID=8YFLogxK
U2 - 10.1016/S0034-4877(06)80963-8
DO - 10.1016/S0034-4877(06)80963-8
M3 - Article
AN - SCOPUS:34548312475
VL - 58
SP - 433
EP - 443
JO - Reports on Mathematical Physics
JF - Reports on Mathematical Physics
SN - 0034-4877
IS - 3
ER -