Model Predictive Control of a Vehicle using Koopman Operator

TL;DR

This paper presents a data-driven approach using the Koopman operator to linearize nonlinear vehicle dynamics for Model Predictive Control, enabling effective control of complex nonlinear behaviors.

Contribution

It introduces a Koopman operator-based linear predictor for nonlinear vehicle models, facilitating linear MPC design for complex nonlinear systems.

Findings

Koopman-based controller effectively manages highly nonlinear vehicle states.

Compared to local linearization, the Koopman approach shows improved recovery from nonlinear states.

The method demonstrates potential for advanced vehicle control applications.

Abstract

This paper continues in the work from arXiv:1903.06103 [math.OC] where a nonlinear vehicle model was approximated in a purely data-driven manner by a linear predictor of higher order, namely the Koopman operator. The vehicle system typically features a lot of nonlinearities such as rigid-body dynamics, coordinate system transformations and most importantly the tire. These nonlinearities are approximated in a predefined subset of the state-space by the linear Koopman operator and used for a linear Model Predictive Control (MPC) design in the high-dimension state space where the nonlinear system dynamics evolve linearly. The result is a nonlinear MPC designed by linear methodologies. It is demonstrated that the Koopman-based controller is able to recover from a very unusual state of the vehicle where all the aforementioned nonlinearities are dominant. The controller is compared with a controller based on a classic local linearization and shortcomings of this approach are discussed.