Over- and Underapproximating Reach Sets for Perturbed Delay Differential Equations

• 成果类型: Article
• 署名作者: Xue, Bai; Wang, Qiuye; Feng, Shenghua; Zhan, Naijun
• 署名单位: Chinese Academy of Sciences; Institute of Software, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2977993
• 发表日期: 2021
• 页码: 283-290
• 关键词: Perturbation methods; reachability analysis; Differential equations; safety; trajectory; DELAYS; Robustness; Boundary reachability methods; homeomorphism property; perturbed delay differential equations (DDEs)

摘要

This article explores reach set computations for perturbed delay differential equations (DDEs). The perturbed DDEs of interest in this article is a class of DDEs whose dynamics are subject to perturbations, and their solutions feature the local homeomorphism property with respect to initial states. Membership in this class of perturbed DDEs is determined by conducting sensitivity analysis of solution mappings with respect to initial states to impose a bound constraint on the time-lag term. The homeomorphism property of solutions to such class of perturbed DDEs enables us to construct over- and underapproximations of reach sets by performing reachability analysis on just the boundaries of their permitted initial sets, thereby permitting an extension of reach set computation methods for ordinary differential equations to perturbed DDEs. Three examples demonstrate the performance of our approach.