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.利用线性矩阵不等式和Gronwall不等式得到了系统随机有界性的充分条件.同时给出了滑模面函数的有限时间可达性分析.最后的数值仿真验证了所提方法的有效性.
The observer-based sliding mode control is investigated for time-delayed singular stochastic systems with the disturbance of fractional Brownian motions.Firstly,a state observer not driven by fractional Brownian motions is designed,and then an integral-type sliding mode surface function is given based on the observer.For the finite-time stochastic boundedness analysis,a new-type Lyapunov function with double integral is constructed to deal with fractional Brownian motions.Utilizing the principle of singular value decomposition,the design problem for the observer gain matrix is considered.Sufficient conditions are derived for the stochastic boundedness by linear matrix inequalities and the Gronwall inequality.And the reachability of the sliding mode surface in a finite time is analyzed.The last numerical simulation is given for the feasibility of the proposed approach.
作者
李明
解静
考永贵
刘震
LI Ming;XIE Jing;KAO Yong-gui;LIU Zhen(School of Information and Control Engineering,Qingdao University of Technology,Qingdao Shandong 266525,China;School of Science,Harbin Institute of Technology(Weihai),Weihai Shandong 264209,China)
出处
《控制理论与应用》
EI
CAS
CSCD
北大核心
2021年第12期1947-1956,共10页
Control Theory & Applications
基金
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。
关键词
分数布朗运动
广义随机系统
观测器
滑模控制
fractional Brownian motion
singular stochastic system
observer
sliding mode control
