Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework

Chaturantabut, Saifon

International Journal of Applied Mathematics and Computer Science, Tome 30 (2020) no. 4, pp. 615-628.

Résumé

This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.

Détail

Keywords: model order reduction, ordinary differential equation, partial differential equation, proper orthogonal decomposition, discrete empirical interpolation method
Mots-clés : redukcja rzędu modelu, równanie różniczkowe zwyczajne, równanie różniczkowe cząstkowe, rozkład ortogonalny

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