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

Ahmet Eren Sertbaş, Tufan Kumbasar

TL;DR

The proposed stable-by-design LPV neural network-based state-space model that simultaneously learns latent states and internal scheduling variables directly from data is proposed, demonstrating the potential of stability-constrained neural LPV identification as a scalable and reliable framework for modeling complex nonlinear 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 \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.

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

TL;DR

The proposed stable-by-design LPV neural network-based state-space model that simultaneously learns latent states and internal scheduling variables directly from data is proposed, demonstrating the potential of stability-constrained neural LPV identification as a scalable and reliable framework for modeling complex nonlinear 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 \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.

Paper Structure

This paper contains 12 sections, 15 equations, 9 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. The NN-Based LPV SS Model
  3. The Encoder Neural Network
  4. The State-Space Generator Neural Network
  5. NN-SS Training Strategy
  6. Data Preparation
  7. Loss Function
  8. Comparative System Identification Results
  9. SysID Performance Analysis of the Two-Tank System
  10. SysID Performance Analysis of the Robot Arm
  11. SysID Performance Analysis of the Power Plant
  12. Conclusion and Future Work

Figures (9)

  • Figure 1: Test RMSE for different methods and training random seeds across model orders on the two-tank dataset.
  • Figure 2: Estimated latent states for the best NN-SS run on the two-tank dataset.
  • Figure 3: Simulation mode for best model seeds in two-tank system.
  • Figure 4: Test RMSE for different methods and training random seeds across model orders on the robot arm dataset.
  • Figure 5: Evaluation of states for best NN-SS seed in robot arm.
  • ...and 4 more figures