Informativity conditions for data-driven control based on input-state data and polyhedral cross-covariance noise bounds

TL;DR

This paper develops new informativity conditions for data-driven control of dynamical systems using input-state data with polyhedral cross-covariance noise bounds, enabling stabilization and quadratic performance guarantees.

Contribution

It introduces polyhedral cross-covariance noise bounds for data informativity analysis, extending previous ellipsoidal bounds to more general polyhedral sets for control design.

Findings

Provides conditions for stabilization using polyhedral noise bounds.

Enables control design via vertex and half-space representations.

Extends data-driven control theory to new noise characterization methods.

Abstract

Modeling and control of dynamical systems rely on measured data, which contains information about the system. Finite data measurements typically lead to a set of system models that are unfalsified, i.e., that explain the data. The problem of data-informativity for stabilization or control with quadratic performance is concerned with the existence of a controller that stabilizes all unfalsified systems or achieves a desired quadratic performance. Recent results in the literature provide informativity conditions for control based on input-state data and ellipsoidal noise bounds, such as energy or magnitude bounds. In this paper, we consider informativity of input-state data for control where noise bounds are defined through the cross-covariance of the noise with respect to an instrumental variable; bounds that were introduced originally as a noise characterization in parameter bounding identification. The considered cross-covariance bounds are defined by a finite number of hyperplanes, which induce a (possibly unbounded) polyhedral set of unfalsified systems. We provide informativity conditions for input-state data with polyhedral cross-covariance bounds for stabilization and $\mathcal{H}_2$/$\mathcal{H}_\infty$ control through vertex/half-space representations of the polyhedral set of unfalsified systems.