A continuous-time fundamental lemma and its application in data-driven optimal control
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916327945404416 |
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| author | Schmitz, Philipp Faulwasser, Timm Rapisarda, Paolo Worthmann, Karl |
| author_facet | Schmitz, Philipp Faulwasser, Timm Rapisarda, Paolo Worthmann, Karl |
| contents | Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result, we rigorously derive error bounds for finite-order polynomial approximations of elements of the system behavior. To this end, we leverage a link between latent variables and flat outputs of controllable systems. Combined with a continuous-time counterpart of the fundamental lemma by Willems et al., we characterize the suboptimality resulting from polynomial approximations in data-driven linear-quadratic optimal control problems. Finally, we draw upon a numerical example to illustrate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A continuous-time fundamental lemma and its application in data-driven optimal control Schmitz, Philipp Faulwasser, Timm Rapisarda, Paolo Worthmann, Karl Optimization and Control Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result, we rigorously derive error bounds for finite-order polynomial approximations of elements of the system behavior. To this end, we leverage a link between latent variables and flat outputs of controllable systems. Combined with a continuous-time counterpart of the fundamental lemma by Willems et al., we characterize the suboptimality resulting from polynomial approximations in data-driven linear-quadratic optimal control problems. Finally, we draw upon a numerical example to illustrate our results. |
| title | A continuous-time fundamental lemma and its application in data-driven optimal control |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2407.12179 |