Data-driven discovery of Koopman eigenfunctions for control

Abstract Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable prediction, estimation, and control of strongly dynamics using theory. The Koopman operator has emerged as principled embedding dynamics, its eigenfunctions establish intrinsic coordinates along which behave linearly. Previous studies used finite-dimensional approximations for model-predictive approaches. In this work, we illustrate fundamental closure issue approach argue it is beneficial first validate then construct reduced-order models these validated eigenfunctions. These form Koopman-invariant subspace by design and, thus, improved predictive power. We show how can be formulated directly discuss benefits caveats perspective. resulting architecture termed Reduced Order Nonlinear Identification Control (KRONIC). It further demonstrated approximated with data-driven regression power series expansions, based on partial differential equation governing infinitesimal generator operator. Validating discovered crucial lightly damped may faithfully extracted from EDMD or an implicit formulation. are particularly relevant control, they correspond nearly conserved quantities associated persistent such Hamiltonian. KRONIC number examples, including (a) system known embedding, (b) variety Hamiltonian systems, (c) high-dimensional double-gyre model ocean mixing.