Informativity Conditions for Multiple Signals: Properties, Experimental Design, and Applications (extended version)

TL;DR

This paper introduces three new informativity conditions for multi-signal data, enabling effective system identification and control design while addressing challenges of prolonged excitation in control signals.

Contribution

It proposes novel informativity conditions for multi-signal data, along with experimental design methods to satisfy these conditions in system identification and control applications.

Findings

Conditions improve least-squares identification accuracy

Methods enable offline and online excitation synthesis

Conditions extend Willems' fundamental lemma

Abstract

Recent studies highlight the importance of persistently exciting condition in single signal sequence for model identification and data-driven control methodologies. However, maintaining prolonged excitation in control signals introduces significant challenges, as continuous excitation can reduce the lifetime of mechanical devices. In this paper, we introduce three informativity conditions for various types of multi-signal data, each augmented by weight factors. We explore the interrelations between these conditions and their rank properties in linear time-invariant systems. Furthermore, we introduce open-loop experimental design methods tailored to each of the three conditions, which can synthesize the required excitation conditions either offline or online, even in the presence of limited information within each signal segment. We demonstrate the effectiveness of these informativity conditions in least-squares identification. Additionally, all three conditions can extend Willems' fundamental lemma and are utilized to assess the properties of the system. Illustrative examples confirm that these conditions yield satisfactory outcomes in both least-squares identification and the construction of data-driven controllers.