Koopman operator theory enables a global linear representation of a given nonlinear dynamical system. However, since an approximation to the Koopman operator cannot fully represent a nonlinear dynamical system, plant-model mismatch inherently exists and negatively influences the performance of control systems. To this end, we present a new approach called offset-free Koopman Lyapunov-based model predictive control (KLMPC) that augments disturbance dynamics to a Koopman-based model to consider the plant-model mismatch in the optimal control problem. The zero steady-state offset condition of the developed framework is also mathematically examined by rigorously investigating the influence of Lyapunov constraints on the equilibrium point of the offset-free KLMPC system.

Koopman 算子理论能够对给定的非线性动力系统进行全局线性表示。然而，由于 Koopman 算子的近似值不能完全表示非线性动力系统，因此工厂模型不匹配固有地存在并对控制系统的性能产生负面影响。为此，我们提出了一种称为无偏移 Koopman Lyapunov 模型预测控制 (KLMPC) 的新方法，该方法将扰动动力学增强到基于 Koopman 的模型中，以考虑最优控制问题中的受控对象模型失配。通过严格研究 Lyapunov 约束对无偏移 KLMPC 系统平衡点的影响，还对所开发框架的零稳态偏移条件进行了数学检查。