随机激励下连续时间马尔科夫跳变非线性系统的平稳响应研究(英文)

作者:Shan-shan PAN;Wei-qiu ZHU;Rong-chun HU;Rong-hua HUAN; 刊名:Journal of Zhejiang University-Science A(Applied Physics & Engineering) 上传者:余立新

【摘要】目的:提出一种预测随机激励下连续时间马尔科夫跳变非线性系统的平稳响应的近似方法。创新点:1.得到了含有马尔科夫跳变参数的关于能量的平均It?方程;2.建立了含有马尔科夫跳变参数的平均It?方程相应的FPK方程。方法:1.将一个随机激励的马尔科夫跳变非线性系统由状态方程转化为等价的It?方程,并根据It?微分法则给出哈密顿量(系统总能量)的It?方程;2.通过随机平均法,得到关于系统能量的平均It?方程;3.推导并求解相应的FPK方程。结论:1.跳变规律对马尔科夫跳变非线性系统随机响应具有重要影响;2.理论结果与数字模拟结果吻合验证了理论方法的准确性。

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1IntroductionTheoperationofcomplexdynamicalsystemsisoftenaccompaniedbyabruptchangesintheircon-figurationscausedbycomponentorinterconnectionfailure,orbytheonsetofenvironmentaldisturbance.WhenthesesuddenchangesintheoperatingrulesoccurinaccordancewithaMarkovprocess,theas-sociatedstochasticsystemisreferredtoasacontinuous-timeMarkovjumpsystem(MJS).MJSshavemanyapplicationsinavarietyoffields,includ-ingairvehicles(StoicaandYaesh,2002),economics(doValandBasar,1999),powersystems(Ugri-novskiiandPota,2005),satellitedynamics(MeskinandKhorasani,2009),andcommunicationsystems(AbdollahiandKhorasani,2011).SinceKatsandKrasovskii(1960),KrasovskiiandLidskii(1961)firstintroducedMJSs,considera-bleattentionhasbeendevotedtotheanalysisandsynthesisofMJSs(Costaetal.,2006;2013).Neces-saryandsufficientconditionsformomentstabilitywereobtainedbymeansofanexplicitformulaforthecorrespondingLyapunovexponentforapiece-wisedeterministicjumplinearsystem(Mariton,1988).Kushner(1967)appliedthe‘almostsuresta-bility’concepttojumplinearsystems.KrasovskiiandLidskii(1961)studiedthelinearquadraticregu-lator(LQR)controlofMarkovjumplinearsystems.Sworder(1969)solvedtheoptimalcontrolproblemwithfinitetimehorizonusingthemaximumprinci-ple.TheergodiccontrolproblemofMJSisstudiedbasedonthedynamicprogrammingprinciple(Ghoshetal.,1997).However,previousstudyonMJSsmainlyfocusedonstabilityandoptimalcon-trol(JiandChizeck,1992;NatacheandVilma,2004;Luo,2006;HuangandNguang,2008).LittleCorrespondingauthorChina(Nos.11272279,11272201,11321202,113

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