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

arXiv: https://arxiv.org/abs/2111.14193 · HTML: https://mlsanity.com/paper/2111.14193/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2021.

## Built on by (most cited first, 1 of 1)

- [Controller Synthesis from Noisy-Input Noisy-Output Data](https://mlsanity.com/paper/2402.02588/) (2024)

## Abstract (arXiv)

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, H_∞ and H2 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.