An input-output continuous-time version of Willems' lemma

TL;DR

This paper introduces a new continuous-time Willems' lemma that enables data-driven system representation using only input-output trajectories without internal state information, allowing for exact system behavior modeling and simulation.

Contribution

It presents a novel continuous-time Willems' lemma relying solely on measured input-output data and exact trajectories, avoiding basis approximations and internal state knowledge.

Findings

Provides necessary and sufficient conditions for data-based trajectory generation.

Shows how to span the full system behavior from input-output data.

Demonstrates application to continuous-time system simulation.

Abstract

We illustrate a novel version of Willems' lemma for data-based representation of continuous-time systems. The main novelties compared to previous works are two. First, the proposed framework relies only on measured input-output trajectories from the system and no internal (state) information is required. Second, our system representation makes use of exact system trajectories, without resorting to orthogonal bases representations and consequent approximations. We first establish sufficient and necessary conditions for data-based generation of system trajectories in terms of suitable latent variables. Subsequently, we reformulate these conditions using measured input-output data and show how to span the full behavior of the system. Furthermore, we show how to use the developed framework to solve the data-based continuous-time simulation problem.