Learning a Contracting KKL-observer with Local Optimal Guarantees
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913123129098240 |
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| author | Galimberti, Clara Lucía Peralez, Johan Astolfi, Daniele Andrieu, Vincent Nadri, Madiha |
| author_facet | Galimberti, Clara Lucía Peralez, Johan Astolfi, Daniele Andrieu, Vincent Nadri, Madiha |
| contents | The Kazantzis-Kravaris-Luenberger (KKL) observer provides a general framework for nonlinear state estimation by immersing the system dynamics into a stable linear or nonlinear latent dynamics. However, the performance of KKL observers relies heavily on the specific choice of these latent dynamics, which is often heuristic. This paper proposes a methodology to learn a KKL observer that combines global stability guarantees with local optimality. We derive a condition on the latent dynamics such that the observer locally mimics the behavior of a Minimum Energy Estimator (Mortensen observer). We then employ Deep Learning to approximate the KKL transformation and the latent dynamics, using neural network architectures that structurally enforce the contraction property. The proposed strategy is validated through numerical simulations on nonlinear benchmarks, demonstrating a good performance in the presence of state and measurement noise. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_13453 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning a Contracting KKL-observer with Local Optimal Guarantees Galimberti, Clara Lucía Peralez, Johan Astolfi, Daniele Andrieu, Vincent Nadri, Madiha Systems and Control The Kazantzis-Kravaris-Luenberger (KKL) observer provides a general framework for nonlinear state estimation by immersing the system dynamics into a stable linear or nonlinear latent dynamics. However, the performance of KKL observers relies heavily on the specific choice of these latent dynamics, which is often heuristic. This paper proposes a methodology to learn a KKL observer that combines global stability guarantees with local optimality. We derive a condition on the latent dynamics such that the observer locally mimics the behavior of a Minimum Energy Estimator (Mortensen observer). We then employ Deep Learning to approximate the KKL transformation and the latent dynamics, using neural network architectures that structurally enforce the contraction property. The proposed strategy is validated through numerical simulations on nonlinear benchmarks, demonstrating a good performance in the presence of state and measurement noise. |
| title | Learning a Contracting KKL-observer with Local Optimal Guarantees |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2605.13453 |