Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework. (English) Zbl 1461.93057
Summary: 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.
MSC:
| 93B11 | System structure simplification |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C20 | Control/observation systems governed by partial differential equations |
| 93C10 | Nonlinear systems in control theory |
Keywords:
model order reduction; contractivity; ordinary differential equations; partial differential equations; proper orthogonal decomposition; discrete empirical interpolation methodSoftware:
ADOL-CReferences:
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