Model fusion for efficient learning of nonlinear dynamical systems

TL;DR

This paper introduces a novel method for efficiently modeling nonlinear dynamical systems by combining multiple linear models with feature lifting and sparse optimization, improving accuracy across wide operating conditions.

Contribution

It proposes a new approach that constructs a parsimonious nonlinear model from multiple linear models and feature lifting, addressing limitations of existing single linear or nonlinear models.

Findings

Effective in capturing nonlinear dynamics across operating ranges

Demonstrated through simulation case studies showing improved accuracy

Reduces complexity with sparse optimization techniques

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.