This paper proposes a novel approach for modeling and controlling nonlinear systems with varying parameters. The approach introduces the use of a parameter-varying Koopman operator (PVKO) in a lifted space, which provides an efficient way to understand system behavior and design control algorithms that account for underlying dynamics and changing parameters. The PVKO builds on a conventional Koopman model by incorporating local time-invariant linear systems through interpolation within the lifted space. This paper outlines a procedure for identifying the PVKO and designing a model predictive control using the identified PVKO model. Simulation results demonstrate that the proposed approach improves model accuracy and enables predictions based on future parameter information. The feasibility and stability of the proposed control approach are analyzed, and their effectiveness is demonstrated through simulation.

翻译：本文提出了一种针对时变参数非线性系统建模与控制的新方法。该方法在提升空间中引入时变参数Koopman算子（PVKO），为理解系统行为并设计考虑底层动力学和参数变化特性的控制算法提供了有效途径。PVKO通过提升空间内的插值技术融合局部时不变线性系统，构建于传统Koopman模型基础之上。本文阐述了PVKO的辨识流程，并设计了基于该模型的预测控制算法。仿真结果表明，所提方法提高了模型精度，并能基于未来参数信息进行预测。同时分析了所提控制方案的可行性与稳定性，并通过仿真验证了其有效性。