An informativity approach to the data-driven algebraic regulator problem

TL;DR

This paper develops a data-driven approach to the algebraic regulator problem, using input-state data to determine when and how a regulator can be designed to ensure output tracking despite unknown system dynamics.

Contribution

It introduces the concept of data informativity for regulator design and provides necessary and sufficient conditions based on finite data sets.

Findings

Established conditions for data informativity in regulator design

Derived formulas for regulators from data

Validated results with extended examples

Abstract

In this paper, the classical algebraic regulator problem is studied in a data-driven context. The endosystem is assumed to be an unknown system that is interconnected to a known exosystem that generates disturbances and reference signals. The problem is to design a regulator so that the output of the (unknown) endosystem tracks the reference signal, regardless of its initial state and the incoming disturbances. In order to do this, we assume that we have a set of input-state data on a finite time-interval. We introduce the notion of data informativity for regulator design, and establish necessary and sufficient conditions for a given set of data to be informative. Also, formulas for suitable regulators are given in terms of the data. Our results are illustrated by means of two extended examples.