Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification

TL;DR

This paper introduces a neural network-based LPV state-space model that ensures stability by design, effectively capturing nonlinear system dynamics and outperforming traditional methods in long-term prediction accuracy.

Contribution

The paper presents a novel stable-by-design neural LPV state-space model that learns latent states and scheduling variables directly from data with guaranteed stability.

Findings

Model matches or surpasses classical subspace methods

Ensures stability through Schur-based parameterization

Improves long-horizon prediction accuracy

Abstract

Accurate modeling of nonlinear systems is essential for reliable control, yet conventional identification methods often struggle to capture latent dynamics while maintaining stability. We propose a \textit{stable-by-design LPV neural network-based state-space} (NN-SS) model that simultaneously learns latent states and internal scheduling variables directly from data. The state-transition matrix, generated by a neural network using the learned scheduling variables, is guaranteed to be stable through a Schur-based parameterization. The architecture combines an encoder for initial state estimation with a state-space representer network that constructs the full set of scheduling-dependent system matrices. For training the NN-SS, we develop a framework that integrates multi-step prediction losses with a state-consistency regularization term, ensuring robustness against drift and improving long-horizon prediction accuracy. The proposed NN-SS is evaluated on benchmark nonlinear systems, and the results demonstrate that the model consistently matches or surpasses classical subspace identification methods and recent gradient-based approaches. These findings highlight the potential of stability-constrained neural LPV identification as a scalable and reliable framework for modeling complex nonlinear systems.