Exact safety verification of hybrid systems using sums-of-squares representation

In this paper we discuss how to generate inductive invariants for safety verification of hybrid systems. A hybrid symbolic-numeric method is presented to compute inequality inductive invariants of the given systems. A numerical invariant of the given system can be obtained by solving a parameterized...

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Bibliographic Details
Published in:Science China. Information sciences 2014-05, Vol.57 (5), p.16-28
Main Authors: Lin, Wang, Wu, Min, Yang, ZhengFeng, Zeng, ZhenBing
Format: Article
Language:English
Subjects:
Algorithms
Computer Science
Hybrid systems
Inequalities
Information Systems and Communication Service
Invariants
Mathematical analysis
Mathematical models
Optimization
Polynomials
Research Paper
Safety
Verification
不变量
优化问题
参数多项式
安全性
安全验证
平方
数值方法
混合动力系统
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Summary:In this paper we discuss how to generate inductive invariants for safety verification of hybrid systems. A hybrid symbolic-numeric method is presented to compute inequality inductive invariants of the given systems. A numerical invariant of the given system can be obtained by solving a parameterized polynomial optimization problem via sum-of-squares （SOS） relaxation. And a method based on Gauss-Newton refinement and rational vector recovery is used to obtain the invariants with rational coefficients, which exactly satisfy the conditions of invariants. Several examples are given to illustrate our algorithm.
ISSN:1674-733X
1869-1919
DOI:10.1007/s11432-013-4961-z