Abstract
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.
Highlights
Data-driven approaches to extract from trajectories of highdimensional systems, parsimonious models capable of balancing accuracy of the prediction with complexity, are an increasingly popular research topic [1]
The input-output reduced-order model (IOROM) algorithm was proposed in [32] to compute a family of state-consistent datadriven low order linear time-invariant (LTI) state-space models which can be directly parameterized by the vector ρ
This is the case of algebraic DMDc (aDMDc), and while it has the advantage that the projection operators are parameter-dependent, an Linear Parameter-Varying (LPV) model is not available and computational efficiency might be compromised
Summary
Data-driven approaches to extract from trajectories of highdimensional systems, parsimonious models capable of balancing accuracy of the prediction with complexity, are an increasingly popular research topic [1]. These objects are well known in the context of model order reduction of linear systems, as they are the main ingredients to perform balanced truncation [14]. Range and null spaces of the proposed oblique projection are defined so that the identified model is (approximately) in balanced coordinates, and projection onto lower-dimensional subspaces will preserve the structures in the data matrices that are most observable and controllable.
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