Over- and Under-Approximations of Reachable Sets With Series Representations of Evolution Functions

• 成果类型: Article
• 署名作者: She, Zhikun; Li, Meilun
• 署名单位: Beihang University; Beihang University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2994019
• 发表日期: 2021
• 页码: 1414-1421
• 关键词: Level set; safety; Taylor series; Benchmark testing; computational modeling; estimation; programming; Evolution functions; Lie derivatives; over; and under-approximations; partial sums of series; reachable sets

摘要

In this article, we investigate both over- and under-approximations of reachable sets for analytic autonomous dynamical systems beyond polynomial dynamics. We start with the concept of evolution function, whose subzero-level set can be used to describe reachable set, and find a series representation of the evolution function with its Lie derivatives. Afterwards, based on the partial sums of this series, two different methodologies are introduced to compute over- and under-approximations of reachable sets, using numerical quantifier elimination for the semi-algebraic constraints and remainder estimation of the partial sum, respectively. Some benchmarks are given, including an eight-dimensional nonpolynomial quadrotor model, to show the advantages of our computational methods over some existing methods in the literature. Especially, our methods also work for nonconvex initial sets.