A System Parametrization for Direct Data-Driven Analysis and Control with Error-in-Variables

TL;DR

This paper introduces a novel data-driven parametrization method for control analysis that accounts for measurement errors, using robust control techniques and SDPs to provide guaranteed system bounds and extendability.

Contribution

It presents a new parametrization approach employing the Sherman-Morrison-Woodbury formula and robust control, enabling direct data-driven analysis and control with error-in-variables.

Findings

Guaranteed upper bounds on system H2-norms using SDPs

Data-dependent conditions for parametrization applicability

Extension potential for various control and system settings

Abstract

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.