  Koopman operator theory enables a global linear representation of a given
nonlinear dynamical system by transforming the nonlinear dynamics into a higher
dimensional observable function space where the evolution of observable
functions is governed by an infinite-dimensional linear operator. For practical
application of Koopman operator theory, various data-driven methods have been
developed to derive lifted state-space models via approximation to the Koopman
operator. Based on approximate models, several Koopman-based model predictive
control (KMPC) schemes have been proposed. However, since a finite-dimensional
approximation to the infinite-dimensional Koopman operator cannot fully
represent a nonlinear dynamical system, plant-model mismatch inherently exists
in these KMPC schemes and negatively influences the performance of control
systems. In this work, we present offset-free Koopman Lyapunov-based model
predictive control (KLMPC) framework that addresses the inherent plant-model
mismatch in KMPC schemes using an offset-free control framework based on a
disturbance estimator approach and ensures feasibility and stability of the
control system by applying Lyapunov constraints to the optimal control problem.
The zero steady-state offset condition of the developed framework is
mathematically examined. The effectiveness of the developed framework is also
demonstrated by comparing the closed-loop results of the proposed offset-free
KLMPC and the nominal KLMPC.
