Control-Oriented Modeling using Koopman Operator: An application to the Cahn-Hilliard Coarsening Problem

Abstract

In this paper, we present results for the data-driven control oriented modeling of complex dynamics that arise in phase separation of multi-phase immiscible system. This phase separation phenomena is modeled using a complicated nonlinear partial differential equations which are not suitable for control. We use simulation data generated from a detailed physics-based model for the data-driven modeling. We employ Koopman-based lifting for the identification of linear models from the data both under controlled and uncontrolled setting. Spectral analysis of Koopman and its adjoint Perron-Frobenius operator helps us identify invariant structure and dominant modes for the reduced-order representation from the data. Simulation results are presented for the reconstruction and validation of the controlled dynamical model.