Dynamic mode decomposition for compressive system identification

October 21, 2017

Abstract: 

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, we integrate and unify two recent innovations that extend DMD to systems with actuation and systems with heavily subsampled measurements.

Compressive System Identification

A major benefit of dynamic mode decomposition is that it provides a physically interpretable and highly extensiblelinear model framework, which enables the incorporation of actuation inputs and sparse output measurements. When combined, these innovations result in the compressive DMD with control (cDMDc) architecture for compressive system identification, where low-order models are identified from input–output measurements. In contrast to traditional system identification, the reduced states of the cDMDc models may be used to reconstruct the high-dimensional state space via compressed sensing, adding physical interpretability to the models. Thus, cDMDc relies on the existence of a few dominant coherent patterns, which in turn facilitates sparse measurements.

Fig 3.

Two-dimensional system with known dynamics: (a) phase portrait (color denotes the progression of time), (b) x-t diagram of inflated high-dimensional system, (c) two orthogonal modes of P and (d) DCT coefficients of the two modes of P.