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

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.

In the previous version of this arXiv article and the corresponding L-CSS article, DOI: 10.1109/LCSYS.2021.3139526, there was a typographical error in equation (21) and (25). The equations contain $P_{-}$, which should be $Y_{-}$. This typo is corrected in this version

References in corpus (2)

• Combining Prior Knowledge and Data for Robust Controller Design
• Trade-offs in learning controllers from noisy data

Cited by in corpus (3)

• Notes on data-driven output-feedback control of linear MIMO systems
• Controller Synthesis from Noisy-Input Noisy-Output Data
• Data-Driven Identification of Attack-free Sensors in Networked Control Systems