Necessary and Sufficient Conditions for Data-driven Model Reference Control

TL;DR

This paper establishes necessary and sufficient data-driven conditions for model reference control, applicable to noiseless and noisy data, without requiring persistently exciting data, advancing the theoretical foundation of data-driven control design.

Contribution

It introduces new data informativity-based conditions for model reference control that do not depend on persistently exciting data, applicable to both noiseless and noisy scenarios.

Findings

Derived conditions for noiseless data control

Extended conditions to noisy data settings

Provided theoretical guarantees for data-driven control

Abstract

The objective of model reference control is to design a controller that regulates the system's behavior so as to match a specified reference model. This paper investigates necessary and sufficient conditions for model reference control from a data-driven perspective, when only a set of data generated by the system is utilized to directly accomplish the matching. Noiseless and noisy data settings are both considered. Notably, all methods we propose build on the concept of data informativity and do not rely on persistently exciting data.