Parameter-Varying Koopman Operator for Nonlinear System Modeling and Control

TL;DR

This paper introduces a parameter-varying Koopman operator approach for modeling and controlling nonlinear systems with changing parameters, enhancing prediction accuracy and control stability.

Contribution

It develops a novel PVKO framework that incorporates local linear models in a lifted space and provides a method for identifying and controlling nonlinear systems with varying parameters.

Findings

Improved model accuracy over traditional Koopman methods

Effective control design using PVKO in simulations

Enhanced prediction capabilities with future parameter information

Abstract

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.