Data-driven Meets Geometric Control: Zero Dynamics, Subspace Stabilization, and Malicious Attacks

TL;DR

This paper introduces data-driven formulas for geometric control tools, enabling the analysis and control of unknown linear systems directly from experimental data, including subspace confinement, zero computation, and attack design.

Contribution

It provides novel data-driven methods to compute invariant subspaces and zeros of unknown systems, bypassing the need for explicit models.

Findings

Successfully computed invariant subspaces from data

Designed undetectable attacks on unknown systems

Developed feedback control for subspace confinement

Abstract

Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the invariant subspaces of interest. In this paper we overcome this limitation by finding data-driven formulas for some of the foundational tools of geometric control. In particular, for an unknown linear system, we show how controlled and conditioned invariant subspaces can be found directly from experimental data. We use our formulas and approach to (i) find a feedback gain that confines the system state within a desired subspace, (ii) compute the invariant zeros of the unknown system, and (iii) design attacks that remain undetectable.