Reachable Set Estimation and Safety Verification of Nonlinear Systems via Iterative Sums of Squares Programming

作     者：LIN Wang YANG Zhengfeng DING Zuohua LIN Wang;YANG Zhengfeng;DING Zuohua

作者机构：School of Information Science and TechnologyZhejiang Sci-Tech UniversityHangzhou 310018China Shanghai Key Laboratory of Trustworthy ComputingEast China Normal UniversityShanghai 200062China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2022年第35卷第3期

页      面：1154-1172页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 071101[理学-系统理论] 

基　　金：supported in part by the National Natural Science Foundation of China under Grant Nos.12171159 and 61772203 in part by the Zhejiang Provincial Natural Science Foundation of China under Grant No.LY20F020020 

主　　题：Computer mathematics reachable set estimation safety verification sums of squares programming 

摘      要：In this paper,the problems of forward reachable set estimation and safety verification of uncertain nonlinear systems with polynomial dynamics are ***,an iterative sums of squares(SOS)programming approach is developed for reachable set *** characterizes the over-approximations of the forward reachable sets by sub-level sets of time-varying Lyapunovlike functions that satisfy an invariance condition,and formulates the problem of searching for the Lyapunov-like functions as a bilinear SOS program,which can be solved via an iterative *** make the over-approximation tight,the proposed approach seeks to minimize the volume of the overapproximation set with a desired ***,the reachable set estimation approach is extended for safety verification,via explicitly encoding the safety constraint such that the Lyapunov-like functions guarantee both reaching and *** efficiency of the presented method is illustrated by some numerical examples.