A System Parametrization for Direct Data-Driven Analysis and Control with Error-in-Variables
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910908687581184 |
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| author | Brändle, Felix Allgöwer, Frank |
| author_facet | Brändle, Felix Allgöwer, Frank |
| contents | In this paper, we present a new parametrization to perform direct data-driven analysis and controller synthesis for the error-in-variables case. To achieve this, we employ the Sherman-Morrison-Woodbury formula to transform the problem into a linear fractional transformation (LFT) with unknown measurement errors and disturbances as uncertainties. For bounded uncertainties, we apply robust control techniques to derive a guaranteed upper bound on the H2-norm of the unknown true system. To this end, a single semidefinite program (SDP) needs to be solved, with complexity that is independent of the amount of data. Furthermore, we exploit the signal-to-noise ratio to provide a data-dependent condition, that characterizes whether the proposed parametrization can be employed. The modular formulation allows to extend this framework to controller synthesis with different performance criteria, input-output settings, and various system properties. Finally, we validate the proposed approach through a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A System Parametrization for Direct Data-Driven Analysis and Control with Error-in-Variables Brändle, Felix Allgöwer, Frank Systems and Control In this paper, we present a new parametrization to perform direct data-driven analysis and controller synthesis for the error-in-variables case. To achieve this, we employ the Sherman-Morrison-Woodbury formula to transform the problem into a linear fractional transformation (LFT) with unknown measurement errors and disturbances as uncertainties. For bounded uncertainties, we apply robust control techniques to derive a guaranteed upper bound on the H2-norm of the unknown true system. To this end, a single semidefinite program (SDP) needs to be solved, with complexity that is independent of the amount of data. Furthermore, we exploit the signal-to-noise ratio to provide a data-dependent condition, that characterizes whether the proposed parametrization can be employed. The modular formulation allows to extend this framework to controller synthesis with different performance criteria, input-output settings, and various system properties. Finally, we validate the proposed approach through a numerical example. |
| title | A System Parametrization for Direct Data-Driven Analysis and Control with Error-in-Variables |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2411.06787 |