Robust Data-Driven Invariant Sets for Nonlinear Systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912989599236096 |
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| author | Kiani, Sahand Lagoa, Constantino M. |
| author_facet | Kiani, Sahand Lagoa, Constantino M. |
| contents | The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute robust polytopic contractive sets for unknown nonlinear systems operating under persistent bounded process noise and state-input constraints. Rather than attempting to identify a single, potentially nominal model, we utilize a finite data set to construct a polytopic consistency set--a rigorous geometric boundary encapsulating all possible system dynamics compatible with the noisy measurements. The core contribution of this work extends an established sufficient condition for λ contractiveness into the data-driven setting. Crucially, we prove that enforcing this condition strictly over the vertices of the consistency set guarantees robust invariance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Data-Driven Invariant Sets for Nonlinear Systems Kiani, Sahand Lagoa, Constantino M. Systems and Control The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute robust polytopic contractive sets for unknown nonlinear systems operating under persistent bounded process noise and state-input constraints. Rather than attempting to identify a single, potentially nominal model, we utilize a finite data set to construct a polytopic consistency set--a rigorous geometric boundary encapsulating all possible system dynamics compatible with the noisy measurements. The core contribution of this work extends an established sufficient condition for λ contractiveness into the data-driven setting. Crucially, we prove that enforcing this condition strictly over the vertices of the consistency set guarantees robust invariance. |
| title | Robust Data-Driven Invariant Sets for Nonlinear Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.00629 |