针对随机控制系统数值解的均方指数输入状态稳定性

祝乔; 崔家瑞; 胡广大

doi:10.3724/SP.J.1004.2013.01360

针对随机控制系统数值解的均方指数输入状态稳定性

doi: 10.3724/SP.J.1004.2013.01360

1.
北京科技大学自动化学院 100083

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出版历程
- 收稿日期: 2012-05-29
- 修回日期: 2012-12-20
- 刊出日期: 2013-08-20

Mean-Square Exponential Input-to-State Stability of Numerical Solutions for Stochastic Control Systems

1.
School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

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Corresponding author: ZHU Qiao

摘要

摘要: 分析了随机控制系统数值解的均方指数输入状态稳定性. 首先, 针对随机控制系统, 随机θ-方法满足有限时间强收敛条件. 然后, 我们证实, 在有限时间强收敛条件下, 随机控制系统是均方指数输入状态稳定的当且仅当随机θ-方法(充分小步长)是均方指数输入状态稳定的. 另外, 对一类满足单边Lipschitz条件的随机控制系统, 有两类隐式欧拉方法(对任意步长)能够继承原系统的均方指数输入状态稳定性. 最后, 一些数值实例证实了本文所获结论的正确性.
- 均方指数输入状态稳定性 /
- 随机控制系统 /
- 随机θ-方法 /
- 强收敛性
Abstract: This paper deals with the mean-square exponential input-to-state stability (exp-ISS) of numerical solutions for stochastic control systems (SCSs). Firstly, it is shown that a finite-time strong convergence condition holds for the stochastic θ-method on SCSs. Then, we can see that the mean-square exp-ISS of an SCS holds if and only if that of the stochastic θ-method (for suffciently small step sizes) is preserved under the finite-time strong convergence condition. Secondly, for a class of SCSs with a one-sided Lipschitz drift, it is proved that two implicit Euler methods (for any step sizes) can inherit the mean-square exp-ISS property of the SCSs. Finally, numerical examples confirm the correctness of the theorems presented in this study.
- Mean-square exponential input-to-state stability /
- stochastic control systems /
- stochastic θ-method /
- strong convergence

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参考文献(20)

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