文章基本信息

标题：Invariant Sets for Switching Affine Systems Subject to Semi-Algebraic Constraints
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作者：Nikolaos Athanasopoulos ; Nikolaos Athanasopoulos ; Raphaël M. Jungers 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2016
卷号：49
期号：18
页码：158-163
DOI：10.1016/j.ifacol.2016.10.156
语种：English
出版社：Elsevier
摘要：Abstract: We study the problem of computing the maximal admissible positively invariant set for discrete time switching affine systems subject to basic semi-algebraic constraints. First, we obtain inner ϵ-approximations of the minimal invariant set. Second, following recent results for switching linear systems (Athanasopoulos and Jungers, 2016), we apply an algebraic lifting on the system and obtain a polyhedral representation of the constraint set. Working on this lifted state space offers two distinct advantages, namely (i) we can verify inclusion of an e-inflation of the minimal invariant set in the constraint set and (ii) under proper assumptions, we can characterize and compute the maximal admissible invariant set, which is also a basic semi-algebraic set. Consequently, we are able to identify and recover admissible invariant sets for switching affine systems even when only non-convex invariant sets exist. The underlying algorithms involve only linear operations and convex hull computations.
关键词：Keywordssemi-algebraic constraintsswitching affine systemsmaximal admissible invariant setminimal invariant setalgorithms