Data-driven feedback stabilisation of nonlinear systems: Koopman-based model predictive control

Abstract

In this work, a predictive control framework is presented for feedback stabilisation of nonlinear systems. To achieve this, we integrate Koopman operator theory with Lyapunov-based model predictive control (LMPC). The main idea is to transform nonlinear dynamics from state-space to function space using Koopman eigenfunctions -- for control affine systems this results in a bilinear model in the (lifted) function space. Then, a predictive controller is formulated in Koopman eigenfunction coordinates which uses an auxiliary Control Lyapunov Function (CLF) based bounded controller as a constraint to ensure stability of the Koopman system. Remarkably, the feedback control design proposed in this work remains completely data-driven and does not require any explicit knowledge of the original system. Furthermore, due to the bilinear structure of the Koopman model, seeking a CLF is no longer a bottleneck for LMPC. Benchmark numerical examples demonstrate the utility of the proposed feedback control design.