On controllability of nonlinear stochastic systems

R. Sakthivel; J. H. Kim; N. I. Mahmudov

doi:10.1016/S0034-4877(06)80963-8

On controllability of nonlinear stochastic systems

R. Sakthivel, J. H. Kim, N. I. Mahmudov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

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	https://doi.org/10.1016/S0034-4877(06)80963-8
Publication status	Published - 2006 Dec

Bibliographical note

Funding Information:
Acknowledgement The work of RS and JHK is supported by Brain Korea 21 project at Yonsei University, 2005.

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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AU - Mahmudov, N. I.

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PY - 2006/12

Y1 - 2006/12

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.

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On controllability of nonlinear stochastic systems

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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