Robust Nonlinear Model Predictive Control Based on the LPV System with Polytopic Uncertainty Identified Using Koopman Operator

Koopman operator-based model predictive control is a data-driven control approach for nonlinear systems with unknown dynamics. However, the modeling error is almost inevitable when using the Koopman operator. To address this issue, an approach for handling modeling errors in the identification of nonlinear systems via the Koopman operator is proposed. The nonlinear system is represented as a linear parameter-varying (LPV) system with polytopic uncertainty whose vertices of the polytope are obtained through a datadriven approach. A robust model predictive controller is designed for the original nonlinear system based on the identified Koopman operator-polytopic LPV system under the worst-case scenarios. The control design is formulated as an optimization problem subject to the specific linear matrix inequality (LMI) constraints, ensuring recursive feasibility and closed-loop stability. The effectiveness of the proposed modeling and control approach is demonstrated through numerical simulations.