Sparse identification of time delay systems via pseudospectral collocation

TL;DR

This paper introduces a computationally efficient method for identifying nonlinear delay systems by approximating them with ODEs using pseudospectral collocation, focusing on the maximum delay to reduce complexity.

Contribution

It proposes a novel approach that simplifies delay system identification by avoiding optimization over all delays, enhancing performance and reducing computational load.

Findings

Effective delay identification with reduced computational cost

Improved accuracy by focusing on maximum delay

Enhanced performance over existing methods

Abstract

We present a pragmatic approach to the sparse identification of nonlinear dynamics for systems with discrete delays. It relies on approximating the underlying delay model with a system of ordinary differential equations via pseudospectral collocation. To minimize the reconstruction error, the new strategy avoids optimizing all possible multiple unknown delays, identifying only the maximum one. The computational burden is thus greatly reduced, improving the performance of recent implementations that work directly on the delay system.