On stochastic linear systems with zonotopic support sets

doi:10.1016/j.automatica.2019.108652

	On stochastic linear systems with zonotopic support sets
	Villanueva, Mario E.; Houska, Boris
	2020-01
发表期刊	AUTOMATICA
ISSN	0005-1098
卷号	111
发表状态	已发表
DOI	10.1016/j.automatica.2019.108652
摘要	This paper analyzes stochastic linear discrete-time processes, whose process noise sequence consists of independent and uniformly distributed random variables on given zonotopes. We propose a cumulant-based approach for approximating both the transient and limit distributions of the associated state sequence. The method relies on a novel class of k-symmetric Lyapunov equations, which are used to construct explicit expressions for the cumulants. The state distribution is recovered via a generalized Gram–Charlier expansion with respect to products of a multivariate variant of Wigner's semicircle distribution using Chebyshev polynomials of the second kind. This expansion converges uniformly, under surprisingly mild conditions, to the exact state distribution of the system. A robust feedback control synthesis problem is used to illustrate the proposed approach. © 2019 Elsevier Ltd
关键词	Feedback control Linear systems Lyapunov functions Polynomials Random processes Robust control Stochastic systemsChebyshev polynomials of the second kind Distributed random variables Limit distribution Lyapunov equation Robust feedback control State distributions State sequences Stochastic linear systems
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收录类别	EI ; SCIE ; SCI
语种	英语
资助项目	[F-0203-14-012] ; National Natural Science Foundation of China[] ; National Natural Science Foundation of China[61473185]
出版者	Elsevier Ltd
EI入藏号	20194807739200
EI主题词	Feedback control ; Linear systems ; Lyapunov functions ; Polynomials ; Random processes ; Robust control ; Stochastic systems
EI分类号	Automatic Control Principles and Applications:731 ; Control Systems:731.1 ; Mathematics:921 ; Algebra:921.1 ; Probability Theory:922.1 ; Systems Science:961
原始文献类型	Journal article (JA)
引用统计
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/104880
专题	信息科学与技术学院_PI研究组_Boris Houska组
通讯作者	Villanueva, Mario E.
作者单位	School of Information Science and Technology, ShanghaiTech University, China
第一作者单位	信息科学与技术学院
通讯作者单位	信息科学与技术学院
第一作者的第一单位	信息科学与技术学院
推荐引用方式 GB/T 7714	Villanueva, Mario E.,Houska, Boris. On stochastic linear systems with zonotopic support sets[J]. AUTOMATICA,2020,111.
APA	Villanueva, Mario E.,&Houska, Boris.(2020).On stochastic linear systems with zonotopic support sets.AUTOMATICA,111.
MLA	Villanueva, Mario E.,et al."On stochastic linear systems with zonotopic support sets".AUTOMATICA 111(2020).