A Unified Bayesian Framework for Data-Driven Smoothing, Prediction, and Control
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909001074081792 |
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| author | Yin, Mingzhou Iannelli, Andrea Nazari, Seyed Ali Müller, Matthias A. |
| author_facet | Yin, Mingzhou Iannelli, Andrea Nazari, Seyed Ali Müller, Matthias A. |
| contents | Extending data-driven algorithms based on Willems' fundamental lemma to stochastic data often requires empirical and customized workarounds. This work presents a unified Bayesian framework for linear systems that provides a systematic and general method for handling stochastic data-driven tasks, including smoothing, prediction, and control, via maximum a posteriori estimation. This framework formulates a unified trajectory estimation problem for the three tasks by specifying different types of trajectory knowledge. Then, a Bayesian problem is solved that optimally combines trajectory knowledge with a data-driven characterization of the trajectory from offline data for correlated input-output uncertainties with elliptical distributions. Under specific conditions, this problem is shown to generalize existing data-driven prediction and control algorithms. Numerical examples demonstrate the performance of the unified approach for all three tasks against other data-driven and system identification approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Unified Bayesian Framework for Data-Driven Smoothing, Prediction, and Control Yin, Mingzhou Iannelli, Andrea Nazari, Seyed Ali Müller, Matthias A. Systems and Control Extending data-driven algorithms based on Willems' fundamental lemma to stochastic data often requires empirical and customized workarounds. This work presents a unified Bayesian framework for linear systems that provides a systematic and general method for handling stochastic data-driven tasks, including smoothing, prediction, and control, via maximum a posteriori estimation. This framework formulates a unified trajectory estimation problem for the three tasks by specifying different types of trajectory knowledge. Then, a Bayesian problem is solved that optimally combines trajectory knowledge with a data-driven characterization of the trajectory from offline data for correlated input-output uncertainties with elliptical distributions. Under specific conditions, this problem is shown to generalize existing data-driven prediction and control algorithms. Numerical examples demonstrate the performance of the unified approach for all three tasks against other data-driven and system identification approaches. |
| title | A Unified Bayesian Framework for Data-Driven Smoothing, Prediction, and Control |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.01475 |