Interpolatory $\mathcal{H}_2$-optimality Conditions for Structured Linear Time-invariant Systems
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909321192800256 |
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| author | Mlinarić, Petar Benner, Peter Gugercin, Serkan |
| author_facet | Mlinarić, Petar Benner, Peter Gugercin, Serkan |
| contents | Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on $\mathcal{L}_2$-optimal reduced-order modeling of stationary parametric problems, in this paper we develop and investigate optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of structured LTI systems, in particular, for second-order, port-Hamiltonian, and time-delay systems. Under certain diagonalizability assumptions, we show that across all these different structured settings, bitangential Hermite interpolation is the common form for optimality, thus proving a unifying optimality framework for structured reduced-order modeling. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_10618 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Interpolatory $\mathcal{H}_2$-optimality Conditions for Structured Linear Time-invariant Systems Mlinarić, Petar Benner, Peter Gugercin, Serkan Numerical Analysis Systems and Control Optimization and Control Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on $\mathcal{L}_2$-optimal reduced-order modeling of stationary parametric problems, in this paper we develop and investigate optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of structured LTI systems, in particular, for second-order, port-Hamiltonian, and time-delay systems. Under certain diagonalizability assumptions, we show that across all these different structured settings, bitangential Hermite interpolation is the common form for optimality, thus proving a unifying optimality framework for structured reduced-order modeling. |
| title | Interpolatory $\mathcal{H}_2$-optimality Conditions for Structured Linear Time-invariant Systems |
| topic | Numerical Analysis Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2310.10618 |