三角翼滚转运动的首次穿越分析  

First-passage analysis of the rolling motion of delta wing

作　　者：彭如月 焦萌倩 黄文韬 蒋贵荣[1] PENG Ruyue;JIAO Mengqian;HUANG Wentao;JIANG Guirong(School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China;School of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]广西师范大学数学与统计学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2020年第6期528-532,共5页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11662001,11562006,11771105);广西自然科学基金(2016GXNSFDA380031,2017GXNSFFA198012,2018GXNSFAA138177);广西高校中青年教师科研基础能力提升项目(2019KY0228)。

摘　　要：为了分析随机因素对滚转运动的影响,研究高斯白噪声位移参数激励下的三角翼滚转运动的稳定性和可靠性问题,利用能量包线随机平均法讨论了系统的局部稳定性,在不稳定情形下对系统实施控制,得到了系统稳定的充分条件,利用后向Kolmogorov方程和广义Pontryagin方程,讨论了首次穿越时间距。数值模拟给出了控制前后系统的随机响应。分析表明,通过控制作用可提高三角翼机体的横向稳定性和可靠性。In order to analyze the influence of random factors on the roll motion,the stability and reliability of the roll motion of delta wing excited by the displacement parameters of Gauss white noise are studied.The local stability of the system is discussed by using the random average method of energy envelope.The system is controlled under the case of unstable situation and the sufficient conditions for the stability of the system are obtained.The backward Kolmogorov equation and the generalized Pontryagin equation are used to discuss the moment of first-passage time.The random responses of the system before and after the control are given by numerical simulation.The analysis shows that the lateral stability and reliability of the delta wing body can be improved by the control effect.

关 键 词：高斯白噪声 三角翼 可靠性 首次穿越 控制律 

分 类 号：O231.3[理学—运筹学与控制论]