Distributionally Robust Model Predictive Control With Koopman Operator

This paper presents a novel methodology for controlling nonlinear systems by integrating Koopman operators with Distributionally Robust Model Predictive Control (KDRMPC). The proposed approach addresses the challenges posed by external disturbances and model uncertainties by modeling these factors as random variables characterized by their first and second-order moment information, which are estimated from empirical data. Initially, the nonlinear system is linearized using the Koopman operator, transforming the control problem into a linear framework that facilitates control design. Subsequently, K-DRMPC is employed to reformulate state chance constraints into Second-Order Cone (SOC) constraints, ensuring robust performance in the presence of uncertainties. Numerical experiments validate the effectiveness of the proposed approach under disturbances.