Koopman Operator-based Model Predictive Control with Recursive Online Update
Horacio M. Calderón, Erik Schulz, Thimo Oehlschlägel, Herbert Werner
Abstract
The Koopman operator framework allows to embed a nonlinear system into a linear one. This enables the analysis, estimation, and control of nonlinear dynamics with linear methods. Controllers based on the Koopman operator (KO) are often model predictive control (MPC) schemes. The performance of an MPC depends on the prediction accuracy of its model. Hence, it is meaningful to update the model online if the predictions are not sufficiently accurate. In this work, we approach this problem by using a recursive least squares (RLS) algorithm with forgetting factor. Furthermore, we show in an empirical case study that combining the KO with an online update and the recently proposed quasi-linear parameter-varying model predictive control (qLMPC) algorithm results in an efficient control scheme.