  A novel approach to reduced-order modeling of high-dimensional time varying
systems is proposed. It leverages the formalism of the Dynamic Mode
Decomposition technique together with the concept of balanced realization. It
is assumed that the only information available on the system comes from input,
state, and output trajectories generated by numerical simulations or recorded
and estimated during experiments, 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. Since the dynamics of
aeroservoelastic systems markedly changes in operation (e.g. due to change in
flight speed or altitude), time-varying features are retained in the
constructed models. This is achieved by generating 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 entirely 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 algorithms recently proposed in the literature.
Comparisons cover both prediction accuracy and performance in model predictive
control applications.
