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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.13371 |
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| _version_ | 1866910080026279936 |
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| author | Doebeli, Carlos Astolfi, Alessandro Kalise, Dante Moreschini, Alessio Scarciotti, Giordano Simard, Joel |
| author_facet | Doebeli, Carlos Astolfi, Alessandro Kalise, Dante Moreschini, Alessio Scarciotti, Giordano Simard, Joel |
| contents | We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed to find an approximate solution to the invariance equation using a Newton iteration on the coefficients of a monomial basis expansion of the solution. These solutions to the invariance equations can then be used to construct reduced-order models. We assess the ability of the method to solve the invariance PDE system as well as to achieve moment matching and recover the steady-state behaviour of nonlinear systems with state dimension of order 1000 driven by linear and nonlinear signal generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A polynomial approximation scheme for nonlinear model reduction by moment matching Doebeli, Carlos Astolfi, Alessandro Kalise, Dante Moreschini, Alessio Scarciotti, Giordano Simard, Joel Optimization and Control Numerical Analysis 49M15, 70Q05, 93A30 We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed to find an approximate solution to the invariance equation using a Newton iteration on the coefficients of a monomial basis expansion of the solution. These solutions to the invariance equations can then be used to construct reduced-order models. We assess the ability of the method to solve the invariance PDE system as well as to achieve moment matching and recover the steady-state behaviour of nonlinear systems with state dimension of order 1000 driven by linear and nonlinear signal generators. |
| title | A polynomial approximation scheme for nonlinear model reduction by moment matching |
| topic | Optimization and Control Numerical Analysis 49M15, 70Q05, 93A30 |
| url | https://arxiv.org/abs/2412.13371 |