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

2025-10-21

AI Summary

Addressing the challenge of simultaneously ensuring model stability and accurate dynamic representation in nonlinear system identification, this paper proposes a neural network-driven stable LPV state-space modeling framework. The method explicitly enforces internal stability of the state transition matrix via Schur parameterization, integrates an encoder–state-space joint architecture to jointly learn latent states and scheduling variables in a data-driven manner, and incorporates a state consistency regularization term to enhance robustness. The model is trained end-to-end by jointly optimizing a multi-step prediction loss and the regularization objective, thereby unifying deep learning with LPV system theory. Experimental evaluation on multiple nonlinear benchmark systems demonstrates that the proposed approach achieves superior long-term prediction accuracy and modeling reliability compared to conventional subspace-based methods and state-of-the-art gradient-based approaches.

Technology Category

• Intelligent Robots: State Estimation
• Natural Language Processing: Learning & Optimization for NLP
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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 extit{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.

Problem

• Modeling nonlinear systems with guaranteed stability constraints
• Learning latent states and scheduling variables from data
• Improving long-horizon prediction accuracy for complex dynamics

Innovation

• Stable LPV neural state-space model learns latent dynamics
• Schur-based parameterization guarantees stable transition matrix
• Multi-step prediction with state-consistency regularization improves accuracy