STABLE SET-VALUED INTEGRATION OF NONLINEAR DYNAMIC SYSTEMS USING AFFINE SET-PARAMETERIZATIONS

doi:10.1137/140976807

	STABLE SET-VALUED INTEGRATION OF NONLINEAR DYNAMIC SYSTEMS USING AFFINE SET-PARAMETERIZATIONS
	Houska, Boris1,2 ; Villanueva, Mario E.1; Chachuat, Benoit 1
	2015
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	53 期号:5 页码:2307-2328
发表状态	已发表
DOI	10.1137/140976807
摘要	Many set-valued integration algorithms for parametric ordinary differential equations (ODEs) implement a combination of Taylor series expansion with either interval arithmetic or Taylor model arithmetic. Due to the wrapping effect, the diameter of the solution-set enclosures computed with these algorithms typically diverges to infinity on finite integration horizons, even though the ODE trajectories themselves may be asymptotically stable. This paper starts by describing a new discretized set-valued integration algorithm that uses a predictor-validation approach to propagate generic affine set-parameterizations, whose images are guaranteed to enclose the ODE solution set. Sufficient conditions are then derived for this algorithm to be locally asymptotically stable, in the sense that the computed enclosures are guaranteed to remain stable on infinite time horizons when applied to a dynamic system in the neighborhood of a locally asymptotically stable periodic orbit (or equilibrium point). The key requirement here is quadratic Hausdorff convergence of function extensions in the chosen affine set-parameterization, which is proved to be the case, for instance, for Taylor models with ellipsoidal remainders. These stability properties are illustrated with the case study of a cubic oscillator system.
关键词	ordinary differential equations reachability analysis affine set-parameterization set-valued integration convergence analysis stability analysis
收录类别	SCI ; EI
语种	英语
资助项目	Engineering and Physical Sciences Research Council[EP/J006572/1]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000364456100009
出版者	SIAM PUBLICATIONS
EI入藏号	20154501503979
EI主题词	Algorithms ; Differential equations ; Dynamical systems ; Enclosures ; Integral equations ; Nonlinear dynamical systems ; Parameter estimation ; Parameterization ; Stability
EI分类号	Mathematics:921 ; Calculus:921.2
WOS关键词	ORDINARY DIFFERENTIAL-EQUATIONS ; DETERMINISTIC GLOBAL OPTIMIZATION ; INITIAL-VALUE PROBLEMS ; VALIDATED SOLUTIONS ; PARAMETRIC ODES ; INEQUALITIES ; RELAXATIONS ; ALGORITHM
原始文献类型	Article
引用统计
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/2314
专题	信息科学与技术学院_PI研究组_Boris Houska组
通讯作者	Chachuat, Benoit
作者单位	1.Univ London Imperial Coll Sci Technol & Med, Dept Chem Engn, Ctr Proc Syst Engn, London SW7 2AZ, England 2.ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai 200031, Peoples R China
第一作者单位	信息科学与技术学院
推荐引用方式 GB/T 7714	Houska, Boris,Villanueva, Mario E.,Chachuat, Benoit. STABLE SET-VALUED INTEGRATION OF NONLINEAR DYNAMIC SYSTEMS USING AFFINE SET-PARAMETERIZATIONS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2015,53(5):2307-2328.
APA	Houska, Boris,Villanueva, Mario E.,&Chachuat, Benoit.(2015).STABLE SET-VALUED INTEGRATION OF NONLINEAR DYNAMIC SYSTEMS USING AFFINE SET-PARAMETERIZATIONS.SIAM JOURNAL ON NUMERICAL ANALYSIS,53(5),2307-2328.
MLA	Houska, Boris,et al."STABLE SET-VALUED INTEGRATION OF NONLINEAR DYNAMIC SYSTEMS USING AFFINE SET-PARAMETERIZATIONS".SIAM JOURNAL ON NUMERICAL ANALYSIS 53.5(2015):2307-2328.