Data-Driven Control for Linear Discrete-Time Delay Systems

TL;DR

This paper introduces data-driven control formulas for linear discrete-time delay systems, enabling stabilization and optimal control design without relying on explicit system models, while addressing uncertainties and noise.

Contribution

It provides novel data-based formulas for control design in delay systems, unifying stabilization, guaranteed cost, and $H_{ ablafty}$ control, with extensions for delay estimation and robustness.

Findings

Effective stabilization of delay systems using data-driven methods

Unified approach for multiple control objectives

Robust control formulas accommodating noisy data

Abstract

The increasing ease of obtaining and processing data together with the growth in system complexity has sparked the interest in moving from conventional model-based control design towards data-driven concepts. Since in many engineering applications time delays naturally arise and are often a source of instability, we contribute to the data-driven control field by introducing data-based formulas for state feedback control design in linear discrete-time time-delay systems with uncertain delays. With the proposed approach, the problems of system stabilization as well as of guaranteed cost and $H_{\infty}$ control design are treated in a unified manner. Extensions to determine the system delays and to ensure robustness in the event of noisy data are also provided.