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Paper details
Number 4 - December 2020
Volume 30 - 2020
Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework
Saifon Chaturantabut
Abstract
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.
Keywords
model order reduction, contractivity, ordinary differential equations, partial differential equations, proper orthogonal decomposition, discrete empirical interpolation method