Identifying Large-Scale Linear Parameter Varying Systems with Dynamic Mode Decomposition Methods
This work addresses a specific bottleneck in control theory for large-scale nonlinear systems, but it is incremental as it builds on existing Dynamic Mode Decomposition methods.
The paper tackled the problem of identifying large-scale Linear Parameter Varying (LPV) systems, which are common in practice but lack efficient data-driven methods, by developing a reduced-order modeling approach called DMD-LPV that achieves identification without performance decay in a discretized linear diffusion equation example.
Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven identification of such systems, the literature is quite scarce in terms of works that tackle the identification of LPV models for large-scale systems. Since large-scale systems are ubiquitous in practice, this work develops a methodology for the local and global identification of large-scale LPV systems based on nonintrusive reduced-order modeling. The developed method is coined as DMD-LPV for being inspired in the Dynamic Mode Decomposition (DMD). To validate the proposed identification method, we identify a system described by a discretized linear diffusion equation, with the diffusion gain defined by a polynomial over a parameter. The experiments show that the proposed method can easily identify a reduced-order LPV model of a given large-scale system without the need to perform identification in the full-order dimension, and with almost no performance decay over performing a reduction, given that the model structure is well-established.