A new perspective on Willems' fundamental lemma: Universality of persistently exciting inputs

Abstract

In this letter, we provide new insight into Willems et al.'s fundamental lemma by studying the concept of universal inputs. An input is called universal if, when applied to any controllable system, it leads to input-output data that parametrizes all finite trajectories of the system. By the fundamental lemma, inputs that are persistently exciting of sufficiently high order are universal. The main contribution of this work is to prove the converse. Therefore, universality and persistency of excitation are equivalent.

6 pages

References in corpus (4)

• On a Stochastic Fundamental Lemma and Its Use for Data-Driven Optimal Control
• Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems
• Data-based Control of Feedback Linearizable Systems
• A quantitative and constructive proof of Willems' Fundamental Lemma and its implications