Data-driven closure for Koopman control of non-linear systems

Data‐driven system identification of nonlinear dynamical systems is a powerful paradigm for the design of efficient and robust controllers. In particular, the data‑driven approximation of the Koopman operator has proven successful for state estimation and closed-loop control. However, the key challenge remains the infinite‐dimensional nature of the true Koopman operator, which necessitates finite‐dimensional approximation. This approximation introduces errors and can undermine control performance. The Mori–Zwanzig (MZ) formalism has been demonstrated to provide a closure for finite‑dimensional Koopman approximations of autonomous systems. This is accomplished by incorporating memory kernels that account for the influence of unresolved observables. In this work, we extend the MZ formalism to non‐autonomous systems and develop a closure strategy particularly for bilinear Koopman representation of control-affine non-linear systems. We demonstrate how the resulting model can be integrated into an adaptive Model Predictive Control (MPC) scheme, yielding a data‐driven control architecture that is both accurate and robust for non-linear systems.