Power-Series Approach to Moment-Matching-Based Model Reduction of MIMO Polynomial Nonlinear Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916908012404736 |
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| author | Huang, Chao Astolfi, Alessandro |
| author_facet | Huang, Chao Astolfi, Alessandro |
| contents | The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the nonlinear PDE characterizing the center manifold into the solutions of a series of recursively defined Sylvester equations. This approach allows yielding nonlinear reduced-order models in very much the same way as in the linear case (e.g. analytically). Algorithms are proposed for obtaining the order and the parameters of the reduced-order models with precision of degree $κ$. The approach also provides new insights into the nonlinear moment matching problem: first, a lower bound for the order of the reduced-order model is obtained, which, in the MIMO case, can be strictly less than the number of matched moments; second, it is revealed that the lower bound is affected by the ratio of the number of the input and output channels; third, it is shown that under mild conditions, a nonlinear reduced-order model can always be constructed with either a linear state equation or a linear output equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_13595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power-Series Approach to Moment-Matching-Based Model Reduction of MIMO Polynomial Nonlinear Systems Huang, Chao Astolfi, Alessandro Systems and Control The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the nonlinear PDE characterizing the center manifold into the solutions of a series of recursively defined Sylvester equations. This approach allows yielding nonlinear reduced-order models in very much the same way as in the linear case (e.g. analytically). Algorithms are proposed for obtaining the order and the parameters of the reduced-order models with precision of degree $κ$. The approach also provides new insights into the nonlinear moment matching problem: first, a lower bound for the order of the reduced-order model is obtained, which, in the MIMO case, can be strictly less than the number of matched moments; second, it is revealed that the lower bound is affected by the ratio of the number of the input and output channels; third, it is shown that under mild conditions, a nonlinear reduced-order model can always be constructed with either a linear state equation or a linear output equation. |
| title | Power-Series Approach to Moment-Matching-Based Model Reduction of MIMO Polynomial Nonlinear Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2508.13595 |