A Note on Data-Driven Control for SISO Feedback Linearizable Systems Without Persistency of Excitation

TL;DR

This paper demonstrates that persistency of excitation is not necessary for data-driven control of SISO feedback linearizable systems, simplifying the control design process and broadening its applicability.

Contribution

It extends previous data-driven control methods by removing the need for persistency of excitation, offering a more practical approach for unknown control gain systems.

Findings

Persistency of excitation is not required for control design.

The new approach simplifies data-driven control implementation.

The results are inspired by works on intelligent PID and observer design.

Abstract

The paper [TF19] proposes a data-driven control technique for single-input single-output feedback linearizable systems with unknown control gain by relying on a persistency of excitation assumption. This note extends those results by showing that persistency of excitation is not necessary. We refer the readers to the papers [TMGA17, TF19] for more background and motivation for the technical results in this note. Conceptually, the results in this note were greatly inspired by the work of Fliess and Join on intelligent PID controllers, e.g., [FJ09]. Technically, we were inspired by the work of Nesic and co-workers on observer and controller design based on approximate models [AN04, NT04] and by the work of Astolfi and Ortega on Immersion and Invariance [AO03].