SIMBa: System Identification Methods leveraging Backpropagation

TL;DR

SIMBa is a machine learning-based toolbox for stable system identification that incorporates known structural properties, outperforming traditional methods and enabling structured nonlinear system identification.

Contribution

The paper introduces novel free parametrizations of Schur matrices within SIMBa, allowing the incorporation of known sparsity patterns and true matrix values without compromising stability.

Findings

Outperforms traditional stable subspace identification methods.

Effectively incorporates known sparsity and true matrix values.

Shows promise for structured nonlinear system identification.

Abstract

This manuscript details and extends the SIMBa toolbox (System Identification Methods leveraging Backpropagation) presented in previous work, which uses well-established Machine Learning tools for discrete-time linear multi-step-ahead state-space System Identification (SI). SIMBa leverages linear-matrix-inequality-based free parametrizations of Schur matrices to guarantee the stability of the identified model by design. In this paper, backed up by novel free parametrizations of Schur matrices, we extend the toolbox to show how SIMBa can incorporate known sparsity patterns or true values of the state-space matrices to identify without jeopardizing stability. We extensively investigate SIMBa's behavior when identifying diverse systems with various properties from both simulated and real-world data. Overall, we find it consistently outperforms traditional stable subspace identification methods, and sometimes significantly, especially when enforcing desired model properties. These results hint at the potential of SIMBa to pave the way for generic structured nonlinear SI. The toolbox is open-sourced on https://github.com/Cemempamoi/simba.