Data-Driven State Observers for Measure-Preserving Systems
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914055739932672 |
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| author | Tang, Wentao |
| author_facet | Tang, Wentao |
| contents | The increasing use of data-driven control strategies gives rise to the problem of learning-based state observation. Motivated by this need, the present work proposes a data-driven approach for the synthesis of state observers for discrete-time nonlinear systems with measure-preserving dynamics. To this end, Kazantzis-Kravaris/Luenburger (KKL) observers are shown to be well-defined, where the observer design boils down to determining a nonlinear injective mapping of states and its pseudo-inverse. For its learning-based construction, the KKL observer is related to the Koopman and Perron-Frobenius operators, defined on a Sobolev-type reproducing kernel Hilbert space (RKHS) on which they are shown to be normal operators and thus have a spectral resolution. Hence, observer synthesis algorithms, based on kernel interpolation/regression routines for the desired injective mapping in the observer and its pseudo-inverse, have been proposed in various settings of available dataset -- (i) many orbits, (ii) single long orbit, and (iii) snapshots. Theoretical error analyses are provided, and numerical studies on a chaotic Lorenz system are demonstrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-Driven State Observers for Measure-Preserving Systems Tang, Wentao Systems and Control Dynamical Systems 37A05, 37C05, 37C40, 47A10, 47B20, 93B28, 93B53 The increasing use of data-driven control strategies gives rise to the problem of learning-based state observation. Motivated by this need, the present work proposes a data-driven approach for the synthesis of state observers for discrete-time nonlinear systems with measure-preserving dynamics. To this end, Kazantzis-Kravaris/Luenburger (KKL) observers are shown to be well-defined, where the observer design boils down to determining a nonlinear injective mapping of states and its pseudo-inverse. For its learning-based construction, the KKL observer is related to the Koopman and Perron-Frobenius operators, defined on a Sobolev-type reproducing kernel Hilbert space (RKHS) on which they are shown to be normal operators and thus have a spectral resolution. Hence, observer synthesis algorithms, based on kernel interpolation/regression routines for the desired injective mapping in the observer and its pseudo-inverse, have been proposed in various settings of available dataset -- (i) many orbits, (ii) single long orbit, and (iii) snapshots. Theoretical error analyses are provided, and numerical studies on a chaotic Lorenz system are demonstrated. |
| title | Data-Driven State Observers for Measure-Preserving Systems |
| topic | Systems and Control Dynamical Systems 37A05, 37C05, 37C40, 47A10, 47B20, 93B28, 93B53 |
| url | https://arxiv.org/abs/2509.20596 |