On data-driven control: informativity of noisy input-output data with cross-covariance bounds

Tom R. V. Steentjes; Mircea Lazar; Paul M. J. Van den Hof

doi:10.1109/lcsys.2021.3139526

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arXiv · 2111.14193

On data-driven control: informativity of noisy input-output data with cross-covariance bounds

Tom R. V. Steentjes·Mircea Lazar·Paul M. J. Van den Hof

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Abstract

In this paper we develop new data informativity based controller synthesis methods that extend existing frameworks in two relevant directions: a more general noise characterization in terms of cross-covariance bounds and informativity conditions for control based on input-output data. Previous works have derived necessary and sufficient informativity conditions for noisy input-state data with quadratic noise bounds via an S-procedure. Although these bounds do not capture cross-covariance bounds in general, we show that the S-procedure is still applicable for obtaining non-conservative conditions on the data. Informativity-conditions for stability, $\mathcal{H}_\infty$ and $\mathcal{H}_2$ control are developed, which are sufficient for input-output data and also necessary for input-state data. Simulation experiments illustrate that cross-covariance bounds can be less conservative for informativity, compared to norm bounds typically employed in the literature.

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Tom R. V. Steentjes, Mircea Lazar, Paul M. J. Van den Hof. 2021-11-28. On data-driven control: informativity of noisy input-output data with cross-covariance bounds. https://doi.org/10.1109/lcsys.2021.3139526

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