The balanced mode decomposition algorithm for data-driven LPV low-order models of aeroservoelastic systems

A novel approach to reduced-order modeling of high-dimensional systems with time-varying properties is proposed. It combines the problem formulation of the Dynamic Mode Decomposition method with the concept of balanced realization. It is assumed that the only information available on the system comes from input, state, and output trajectories, thus the approach is fully data-driven. The goal is to obtain an input-output low dimensional linear model which approximates the system across its operating range. Time-varying features of the system are retained by means of a Linear Parameter-Varying representation made of a collection of state-consistent linear time-invariant reduced-order models. The algorithm formulation hinges on the idea of replacing the orthogonal projection onto the Proper Orthogonal Decomposition modes, used in Dynamic Mode Decomposition-based approaches, with a balancing oblique projection constructed from data. As a consequence, the input-output information captured in the lower-dimensional representation is increased compared to other projections onto subspaces of same or lower size. Moreover, a parameter-varying projection is possible while also achieving state-consistency. The validity of the proposed approach is demonstrated on a morphing wing for airborne wind energy applications by comparing the performance against two recent algorithms. Analyses account for both prediction accuracy and closed-loop performance in model predictive control applications. (C) 2021 The Author(s). Published by Elsevier Masson SAS.

Automated summary

This novel approach combines Dynamic Mode Decomposition with balanced realization to achieve reduced-order modeling of high-dimensional systems with time-varying properties in a fully data-driven manner. The goal is to obtain a low-dimensional linear model approximating the system within its operating range, while retaining time-varying features through a collection of state-consistent linear time-invariant reduced-order models. The method replaces orthogonal projection with a balancing oblique projection constructed from data to increase input-output information captured in the lower-dimensional representation.