Robust stability analysis of a simple data-driven model predictive control approach
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866915044784078848 |
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| author | Bongard, Joscha Berberich, Julian Köhler, Johannes Allgöwer, Frank |
| author_facet | Bongard, Joscha Berberich, Julian Köhler, Johannes Allgöwer, Frank |
| contents | In this paper, we provide a theoretical analysis of closed-loop properties of a simple data-driven model predictive control (MPC) scheme. The formulation does not involve any terminal ingredients, thus allowing for a simple implementation without (potential) feasibility issues. The proposed approach relies on an implicit description of linear time-invariant systems based on behavioral systems theory, which only requires one input-output trajectory of an unknown system. For the nominal case with noise-free data, we prove that the data-driven MPC scheme ensures exponential stability for the closed loop if the prediction horizon is sufficiently long. Moreover, we analyze the robust data-driven MPC scheme for noisy output measurements for which we prove closed-loop practical exponential stability. The advantages of the presented approach are illustrated with a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_00851 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Robust stability analysis of a simple data-driven model predictive control approach Bongard, Joscha Berberich, Julian Köhler, Johannes Allgöwer, Frank Optimization and Control Systems and Control In this paper, we provide a theoretical analysis of closed-loop properties of a simple data-driven model predictive control (MPC) scheme. The formulation does not involve any terminal ingredients, thus allowing for a simple implementation without (potential) feasibility issues. The proposed approach relies on an implicit description of linear time-invariant systems based on behavioral systems theory, which only requires one input-output trajectory of an unknown system. For the nominal case with noise-free data, we prove that the data-driven MPC scheme ensures exponential stability for the closed loop if the prediction horizon is sufficiently long. Moreover, we analyze the robust data-driven MPC scheme for noisy output measurements for which we prove closed-loop practical exponential stability. The advantages of the presented approach are illustrated with a numerical example. |
| title | Robust stability analysis of a simple data-driven model predictive control approach |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2103.00851 |