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Embedding Method by Real Numerical Algebraic Geometry for Structurally Unamenable Differential-Algebraic Equations
Yang, Wenqiang1,2; Wu, Wenyuan1; Reid, Greg3
2024-09-14
摘要Existing structural analysis methods may fail to identify all hidden constraints in systems of differential-algebraic equations with parameters, particularly when the system is structurally unamenable for certain parameter values. In this paper, the authors address numerical methods for polynomial systems of differential-algebraic equations using numerical real algebraic geometry to resolve such issues. Initially, the authors propose an embedding method that constructs an equivalent system with a full-rank Jacobian matrix for any given real analytic system. Secondly, the authors introduce a witness point method, which assists in detecting the constant rank of a component of the constraints in such systems. Finally, these two methods lead to a comprehensive numerical global structural analysis method for polynomial differential-algebraic equations across all components of constraints.
关键词Constant rank differential-algebraic equations real algebraic geometry structural analysis witness point
DOI10.1007/s11424-024-4048-5
发表期刊JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN1009-6124
页码24
通讯作者Wu, Wenyuan(wuwenyuan@cigit.ac.cn)
收录类别SCI
WOS记录号WOS:001312095400001
语种英语