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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.29013 |
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| _version_ | 1866910267430928384 |
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| author | Yang, Yi Lopez, Victor G. Müller, Matthias A. |
| author_facet | Yang, Yi Lopez, Victor G. Müller, Matthias A. |
| contents | In this paper, we propose a moving horizon estimation (MHE)-based training method for feedforward neural networks (FNNs) with rectified linear unit (ReLU) activation functions to determine their ideal weights from a control-theoretic perspective. This allows for a rigorous theoretical analysis of the trained network. First, we reformulate the FNN as a dynamical system with the weights as states. Then, we investigate the local observability of such a system. For two-layer FNNs with fixed output weights, we derive a sufficient condition under which the observability rank condition holds, ensuring a locally observable state. We also show that multi-layer FNNs in general fail to satisfy the observability rank condition. Based on this analysis, we develop a persistently exciting (PE) input design method, which renders a state distinguishable from its neighbors. The resulting local observability provides convergence guarantees for the proposed MHE-based training, where only the projection of the state onto the observable subspace is updated using a fixed-length window of input-output data. The effectiveness of the approach is illustrated via numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29013 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local Observability and Moving Horizon Estimation-based Training of Feedforward Neural Networks Yang, Yi Lopez, Victor G. Müller, Matthias A. Systems and Control In this paper, we propose a moving horizon estimation (MHE)-based training method for feedforward neural networks (FNNs) with rectified linear unit (ReLU) activation functions to determine their ideal weights from a control-theoretic perspective. This allows for a rigorous theoretical analysis of the trained network. First, we reformulate the FNN as a dynamical system with the weights as states. Then, we investigate the local observability of such a system. For two-layer FNNs with fixed output weights, we derive a sufficient condition under which the observability rank condition holds, ensuring a locally observable state. We also show that multi-layer FNNs in general fail to satisfy the observability rank condition. Based on this analysis, we develop a persistently exciting (PE) input design method, which renders a state distinguishable from its neighbors. The resulting local observability provides convergence guarantees for the proposed MHE-based training, where only the projection of the state onto the observable subspace is updated using a fixed-length window of input-output data. The effectiveness of the approach is illustrated via numerical examples. |
| title | Local Observability and Moving Horizon Estimation-based Training of Feedforward Neural Networks |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2605.29013 |