Learning Reduced-Order Linear Parameter-Varying Models of Nonlinear Systems

TL;DR

This work introduces a data-driven method to learn a global reduced-order LPV model ($ROLPVM$) of a nonlinear system by first learning a nonlinear state-projection and then fitting a scheduling-dependent LPV model via neural networks. The two-step procedure yields a structured, global LPV representation on a reduced state, enabling LPV-based analysis and controller design while capturing nonlinear dynamics more accurately than local or linear projections. Empirical results on a CMG and a large MSD interconnection demonstrate improved state reconstruction and prediction accuracy, with substantial gains over baseline methods that rely on linear projections or local models. The approach offers a practical pathway to scalable, controllable reduced-order modeling for complex nonlinear systems, with future work aiming at simultaneously learning the projection and LPV structure.

Abstract

In this paper, we consider the learning of a Reduced-Order Linear Parameter-Varying Model (ROLPVM) of a nonlinear dynamical system based on data. This is achieved by a two-step procedure. In the first step, we learn a projection to a lower dimensional state-space. In step two, an LPV model is learned on the reduced-order state-space using a novel, efficient parameterization in terms of neural networks. The improved modeling accuracy of the method compared to an existing method is demonstrated by simulation examples.

Figures (4)

• Figure 1: The architecture for state-projection.
• Figure 2: LPV-NN architecture for learning the ROLPVM.
• Figure 3: Noise infected output of the CMG ( ), noiseless output ( ), and learned ROLPVM ( ).
• Figure 4: Output of the MSD ( ), learned ROLPVM ( ), and result of (Annoni et al., 2017) ( ).