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arXiv · 2111.08160

Embedding Method by Real Numerical Algebraic Geometry for Structurally Unamenable Differential-Algebraic Equations

Wenqiang Yang·Wenyuan Wu·Greg Reid
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Abstract

Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for polynomial systems of differential-algebraic equations, numerical methods are given to solve such cases using numerical real algebraic geometry. First, we propose an embedding method that for a given real analytic system constructs an equivalent system with a full-rank Jacobian matrix. Secondly, we introduce a witness point method, which can help to detect degeneration on all components of constraints of such systems. Thirdly, the two methods above lead to a numerical global structural analysis method for structurally unamenable differential-algebraic equations on all components of constraints.

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Wenqiang Yang, Wenyuan Wu, Greg Reid. 2021-11-16. Embedding Method by Real Numerical Algebraic Geometry for Structurally Unamenable Differential-Algebraic Equations. https://arxiv.org/abs/2111.08160

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