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Model fusion for efficient learning of nonlinear dynamical systems

Vatsal Kedia, Vivek S. Pinnamaraju, Dinesh Patil

TL;DR

The paper tackles learning nonlinear dynamics across wide operating regions by fusing multiple locally linear models into a global nonlinear p-NARX representation. It leverages lifting to create nonlinear features from linear-model simulations and enforces sparsity via Elastic-net to obtain a compact, interpretable model, followed by re-identification for robust parameters. Across toy, conical-tank, and Hammerstein–Wiener case studies, the approach achieves substantially better intermediate-point predictions than individual local models, while avoiding additional plant experiments. The method enables reliable nonlinear modeling suitable for control applications (e.g., nonlinear MPC) and offers a practical path toward broader operating-range models, with potential extensions to MIMO systems.

Abstract

In the context of model-based control of industrial processes, it is a common practice to develop a data-driven linear dynamical model around a specified operating point. However, in applications involving wider operating conditions, representation of the dynamics using a single linear dynamic model is often inadequate, requiring either a nonlinear model or multiple linear models to accommodate the nonlinear behaviour. While the development of the former suffers from the requirements of extensive experiments spanning multiple levels, significant compromise in the nominal product quality and dealing with unmeasured disturbances over wider operating conditions, the latter faces the challenge of model switch scheduling and inadequate description of dynamics for the operating regions in-between. To overcome these challenges, we propose an efficient approach to obtain a parsimonious nonlinear dynamic model by developing multiple linear models from data at multiple operating points, lifting the data features obtained from individual model simulations to adequately accommodate the underlying nonlinear behaviour and finally, sparse optimization techniques to obtain a parsimonious model. The performance and effectiveness of the proposed algorithm is demonstrated through simulation case studies.

Model fusion for efficient learning of nonlinear dynamical systems

TL;DR

The paper tackles learning nonlinear dynamics across wide operating regions by fusing multiple locally linear models into a global nonlinear p-NARX representation. It leverages lifting to create nonlinear features from linear-model simulations and enforces sparsity via Elastic-net to obtain a compact, interpretable model, followed by re-identification for robust parameters. Across toy, conical-tank, and Hammerstein–Wiener case studies, the approach achieves substantially better intermediate-point predictions than individual local models, while avoiding additional plant experiments. The method enables reliable nonlinear modeling suitable for control applications (e.g., nonlinear MPC) and offers a practical path toward broader operating-range models, with potential extensions to MIMO systems.

Abstract

In the context of model-based control of industrial processes, it is a common practice to develop a data-driven linear dynamical model around a specified operating point. However, in applications involving wider operating conditions, representation of the dynamics using a single linear dynamic model is often inadequate, requiring either a nonlinear model or multiple linear models to accommodate the nonlinear behaviour. While the development of the former suffers from the requirements of extensive experiments spanning multiple levels, significant compromise in the nominal product quality and dealing with unmeasured disturbances over wider operating conditions, the latter faces the challenge of model switch scheduling and inadequate description of dynamics for the operating regions in-between. To overcome these challenges, we propose an efficient approach to obtain a parsimonious nonlinear dynamic model by developing multiple linear models from data at multiple operating points, lifting the data features obtained from individual model simulations to adequately accommodate the underlying nonlinear behaviour and finally, sparse optimization techniques to obtain a parsimonious model. The performance and effectiveness of the proposed algorithm is demonstrated through simulation case studies.
Paper Structure (13 sections, 12 equations, 5 figures, 2 tables, 1 algorithm)

This paper contains 13 sections, 12 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem formulation
  3. Polynomial NARX model (p-NARX)
  4. Problem formulation
  5. Model Fusion: Learning nonlinear dynamics
  6. Linear features
  7. Appending non-linear features and feature selection
  8. Model re-identification and validation
  9. Case Studies
  10. Toy example
  11. Conical tank process
  12. Hammerstein-Wiener models
  13. Conclusion

Figures (5)

  • Figure 1: Toy example: Different behaviour at two operating points
  • Figure 2: Comparison of model predictions at new operating point (us = 0.2)
  • Figure 3: Conical tank: Different behaviour at two operating points
  • Figure 4: Comparison of model predictions at new operating point (7.5 cm)
  • Figure 5: Comparison of model predictions at new operating point (us = 0.5)