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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2603.16851 |
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| _version_ | 1866914402792374272 |
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| author | Mojahed, Navid Rabbani, Mahdis Nazari, Shima |
| author_facet | Mojahed, Navid Rabbani, Mahdis Nazari, Shima |
| contents | We propose a data-driven linear modeling framework for controlled nonlinear hereditary systems that combines Koopman lifting with a truncated Grunwald-Letnikov memory term. The key idea is to model nonlinear state dependence through a lifted observable representation while imposing history dependence directly in the lifted coordinates through fixed fractional-difference weights. This preserves linearity in the lifted state-transition and input matrices, yielding a memory-compensated regression that can be identified from input-state data by least squares and extending standard Koopman-based identification beyond the Markovian setting. We further derive an equivalent augmented Markovian realization by stacking a finite window of lifted states, thereby rewriting the finite-memory recursion as a standard discrete-time linear state-space model. Numerical experiments on a nonlinear hereditary benchmark with a non-Grunwald-Letnikov Prony-series ground-truth kernel demonstrate improved multi-step open-loop prediction accuracy relative to memoryless Koopman and non-lifted state-space baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16851 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Koopman Lifted Finite Memory Identification via Truncated Grunwald Letnikov Kernels Mojahed, Navid Rabbani, Mahdis Nazari, Shima Systems and Control Optimization and Control 93B30, 26A33, 93C10 We propose a data-driven linear modeling framework for controlled nonlinear hereditary systems that combines Koopman lifting with a truncated Grunwald-Letnikov memory term. The key idea is to model nonlinear state dependence through a lifted observable representation while imposing history dependence directly in the lifted coordinates through fixed fractional-difference weights. This preserves linearity in the lifted state-transition and input matrices, yielding a memory-compensated regression that can be identified from input-state data by least squares and extending standard Koopman-based identification beyond the Markovian setting. We further derive an equivalent augmented Markovian realization by stacking a finite window of lifted states, thereby rewriting the finite-memory recursion as a standard discrete-time linear state-space model. Numerical experiments on a nonlinear hereditary benchmark with a non-Grunwald-Letnikov Prony-series ground-truth kernel demonstrate improved multi-step open-loop prediction accuracy relative to memoryless Koopman and non-lifted state-space baselines. |
| title | Koopman Lifted Finite Memory Identification via Truncated Grunwald Letnikov Kernels |
| topic | Systems and Control Optimization and Control 93B30, 26A33, 93C10 |
| url | https://arxiv.org/abs/2603.16851 |