A harmonic framework for the identification of linear time-periodic systems

TL;DR

This paper introduces a harmonic modeling approach for identifying linear time-periodic systems in continuous time, converting them into infinite-dimensional LTI systems and reducing the problem to a finite-dimensional least-squares solution.

Contribution

The paper presents a novel harmonic framework that simplifies LTP system identification by avoiding derivatives and leveraging Toeplitz structures and regularization.

Findings

Effective in noisy environments

Accurate approximation with small error

Avoids derivative computation in continuous-time

Abstract

This paper presents a novel approach for the identification of linear time-periodic (LTP) systems in continuous time. This method is based on harmonic modeling and consists in converting any LTP system into an equivalent LTI system with infinite dimension. Leveraging specific harmonic properties, we demonstrate that solving this infinite-dimensional identification problem can be reduced to solving a finitedimensional linear least-squares problem. The result is an approximation of the original solution with an arbitrarily small error. Our approach offers several significant advantages. The first one is closely tied to the harmonic system's inherent LTI characteristic, along with the Toeplitz structure exhibited by its elements. The second advantage is related to the regularization property achieved through the integral action when computing the phasors from input and state trajectories. Finally, our method avoids the computation of signals' derivative. This sets our approach apart from existing methods that rely on such computations, which can be a notable drawback, especially in continuous-time settings. We provide numerical simulations that convincingly demonstrate the effectiveness of the proposed method, even in scenarios where signals are corrupted by noise.