Relative controllability of stochastic nonlinear systems with delay in control

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• 作者：Lijuan Shen^a ; ^b ; Jitao Sun^a ; ^{sunjt@sh163.net} ; ^{sunjt@tongji.edu.cn}
• 关键词：Relative controllability ; Stochastic differential systems ; Delayed controls ; Banach fixed point theorem
• 刊名：Nonlinear Analysis ; Real World Applications
• 出版年：2012
• 期刊代码：44_14681218
• 类别：mt
• 出版时间：December, 2012
• 卷：13
• 期：6
• 页码：2880-2887
• 文件大小：233 K

摘要

The existence of solutions to systems is a natural premise to carry our study about controllability. Under the basic and readily verified conditions to guarantee the existence of the solutions to a system, in this paper, we prove the relative controllability (approximate controllability ) of the stochastic differential systems with delay in control. Sufficient conditions are given firstly for the relative controllability and relative approximate controllability in finite dimensional spaces, and these results are then generalized to infinite-dimensional Hilbert spaces. Finally, examples are given to illustrate the effectiveness of the proposed methods.