  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.
