Integration of offset-free control framework with Koopman Lyapunov-based model predictive control

Abstract

Koopman operator is an infinite-dimensional linear operator that governs the evolution of observable functions along trajectories of a given nonlinear dynamical system. Recently, several predictive control methods utilizing data-driven approximation of Koopman operator have been developed and applied in various fields. However, since a finite-dimensional approximation of Koopman operator cannot fully represent nonlinear dynamics of the original system, the performance of Koopman-based model predictive control (KMPC) system has been negatively impacted by inherent plant-model mismatch. In this study, we present offset-free Koopman Lyapunov-based MPC (KLMPC) to address the inherent plant-model mismatch while guaranteeing feasibility and stability of the control system. The effectiveness of the proposed scheme is demonstrated by a numerical example. Additionally, the zero steady-state offset condition of the proposed method is mathematically analyzed.