Guaranteed $\mathcal{H}_\infty$ performance analysis and controller synthesis for interconnected linear systems from noisy input-state data

TL;DR

This paper develops a data-driven method for guaranteed $ ext{H}_ extinfty$ performance analysis and distributed controller synthesis for interconnected linear systems using noisy input-state data, enabling scalable control of large systems.

Contribution

It extends recent data-based performance analysis to interconnected systems, providing new LMI conditions for distributed control from noisy data.

Findings

Provides LMI conditions for guaranteed $ ext{H}_ extinfty$ performance.

Enables scalable analysis and control of large interconnected systems.

Supports distributed controller synthesis from noisy data.

Abstract

The increase in available data and complexity of dynamical systems has sparked the research on data-based system performance analysis and controller design. Recent approaches can guarantee performance and robust controller synthesis based on noisy input-state data of a single dynamical system. In this paper, we extend a recent data-based approach for guaranteed performance analysis to distributed analysis of interconnected linear systems. We present a new set of sufficient LMI conditions based on noisy input-state data that guarantees $\mathcal{H}_\infty$ performance and have a structure that lends itself well to distributed controller synthesis from data. Sufficient LMI conditions based on noisy data are provided for the existence of a dynamic distributed controller that achieves $\mathcal{H}_\infty$ performance. The presented approach enables scalable analysis and control of large-scale interconnected systems from noisy input-state data sets.