Data-Driven Robust Control for Discrete Linear Time-Invariant Systems: A Descriptor System Approach

TL;DR

This paper introduces a data-driven robust control method for unknown LTI systems affected by noise, using a descriptor system approach to design stabilizing controllers with guaranteed ${H_}$ performance.

Contribution

It develops a two-step data-driven control framework that transforms unknown LTI systems into descriptor systems for robust controller design.

Findings

The method effectively stabilizes unknown LTI systems.

Controllers guarantee ${H_}$ performance.

Simulation demonstrates the approach's effectiveness.

Abstract

Given the recent surge of interest in data-driven control, this paper proposes a two-step method to study robust data-driven control for a parameter-unknown linear time-invariant (LTI) system that is affected by energy-bounded noises. First, two data experiments are designed and corresponding data are collected, then the investigated system is equivalently written into a data-based descriptor system with structured parametric uncertainties. Second, combined with model-based control theory for descriptor systems, state feedback controllers are designed for such data-based descriptor system, which stabilize the original LTI system and guarantee the ${H_\infty}$ performance. Finally, a simulation example is provided to illustrate the effectiveness and merits of our method.