Lifted Bilinear Model-based Linear Model Predictive Control with Scalability

Abstract

We propose a novel linear model predictive control (MPC) using a lifted bilinear model based on Koopman theory, which is computationally scalable against the dimension of the target system and the prediction horizon length. In MPC, the accuracy of the prediction model determines control performance, but it is a challenge to reduce the computational cost especially when considering nonlinearity of the model. To address this, a method has been proposed which represents the nonlinear input affine system as a lifted bilinear model and utilizes linear approximation and prediction error correction regarding the lifted state to achieve a low-computational-cost linear MPC with equivalent performance to nonlinear MPC. However, although the previous studies have shown its effectiveness for relatively low-order systems, it has not been applied to practical systems with higher dimensions. In this study, we extend the conventional method and propose a scalable linear MPC using a lifted bilinear model and apply it to higher-order nonlinear systems. In this paper, a quadrotor system operating in three-dimensional space is considered and its analytical lifted bilinear model is derived. In the formulation of linear MPC using the lifted bilinear model, an error correction method is newly introduced to feedback error for adjustment of the numerical relationships among the elements in the lifted state. The effectiveness of the proposed method is demonstrated through numerical simulations.