Robust Tracking Model Predictive Control with Koopman Operators

Abstract

Koopman operators can be used to lift nonlinear dynamics into a higher dimensional space to obtain a linear model with nonlinear basis functions. They have proven particularly attractive when combined with data-driven techniques to identify the basis function coefficients. The resulting higherorder linear model is subsequently a good candidate for MPC application, as convex solvers may be applied in the lifted space. Nonetheless, the modeling errors between the original nonlinear system and the approximated Koopman linear model must be taken into account in the MPC design such that the closed-loop properties such as recursive feasibility and convergence can be guaranteed. In this paper, we u..