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分数布朗运动干扰下广义随机系统滑模控制
引用本文:李明,解静,考永贵,刘震. 分数布朗运动干扰下广义随机系统滑模控制[J]. 控制理论与应用, 2021, 38(12): 1947-1956
作者姓名:李明  解静  考永贵  刘震
作者单位:青岛理工大学信息与控制工程学院,山东青岛266525;哈尔滨工业大学(威海)理学院,山东威海264209
基金项目:国家自然科学基金项目(61703226), 山东省自然科学基金项目(ZR2020ZD27)资助.
摘    要:本文考虑分数布朗运动干扰下时滞广义随机系统的基于观测器的滑模控制.首先设计了不受分数布朗运动干扰的状态观测器,然后给出了基于观测器的积分型滑模面函数的定义.为了研究观测器系统有限时间随机有界性,构造了带有二重积分的新型Lyapunov函数来处理分数布朗运动.利用奇异值分解原理,解决了观测器增益矩阵设计问题.利用线性矩阵...

关 键 词:分数布朗运动  广义随机系统  观测器  滑模控制
收稿时间:2020-06-24
修稿时间:2021-10-05

Sliding mode control for singular stochastic systems under fractional Brownian motions
LI Ming,XIE Jing,KAO Yong-gui and LIU Zhen. Sliding mode control for singular stochastic systems under fractional Brownian motions[J]. Control Theory & Applications, 2021, 38(12): 1947-1956
Authors:LI Ming  XIE Jing  KAO Yong-gui  LIU Zhen
Affiliation:Qingdao University of Technology,Qingdao University of Technology,Harbin Institute of Technology,Qingdao University of Technology
Abstract:The observer-based sliding mode control is investigated for time-delayed singular stochastic systems withthe disturbance of fractional Brownian motions. Firstly, a state observer not driven by fractional Brownian motions isdesigned, and then an integral-type sliding mode surface function is given based on the observer. For the finite-timestochastic boundedness analysis, a new-type Lyapunov function with double integral is constructed to deal with fractionalBrownian motions. Utilizing the principle of singular value decomposition, the design problem for the observer gainmatrix is considered. Sufficient conditions are derived for the stochastic boundedness by linear matrix inequalities andthe Gronwall inequality. And the reachability of the sliding mode surface in a finite time is analyzed. The last numericalsimulation is given for the feasibility of the proposed approach.
Keywords:fractional Brownian motion   singular stochastic system   observer   sliding mode control
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