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A system parametrization for direct data-driven analysis and control with error-in-variables
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DOI：10.1016/j.ejcon.2025.101307.png)
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Abstract
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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 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 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.
Keywords:
Identification for control
Robust control
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