| 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.[点击复制] |
| LI Ming,XIE Jing,KAO Yong-gui,LIU Zhen.Sliding mode control for singular stochastic systems under fractional Brownian motions[J].Control Theory and Technology,2021,38(12):1947~1956.[点击复制] |
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| 分数布朗运动干扰下广义随机系统滑模控制 |
| Sliding mode control for singular stochastic systems under fractional Brownian motions |
| 摘要点击 1122 全文点击 350 投稿时间：2020-06-24 修订日期：2021-10-05 |
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| DOI编号 10.7641/CTA.2021.00388 |
| 2021,38(12):1947-1956 |
| 中文关键词 分数布朗运动 广义随机系统 观测器 滑模控制 |
| 英文关键词 fractional Brownian motion singular stochastic system observer sliding mode control |
| 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. |
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| 中文摘要 |
| 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. |
| 英文摘要 |
| 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. |