Predictive Direct Yaw Moment Control Based on the Koopman Operator

Abstract

In this brief, we propose a predictive algorithm for direct yaw moment control (DYC) in which a vehicle model is identified by a finite-dimensional approximation of the Koopman operator. The Koopman operator is a linear predictor for nonlinear dynamical systems based on raising the nonlinear dynamics into a higher-dimensional space where its evolution is linear. A novel method for the finite-dimensional numerical approximation of the Koopman operator is proposed, called enhanced extended dynamic mode decomposition (E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DMD). This method allows the reduction of the basis dimension, determined by a user-defined dictionary of observable functions, to achieve a trade-off between model complexity and accuracy. The E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DMD Koopman vehicle model was obtained from the dataset generated by simulating different scenarios using the nonlinear vehicle model and was then used to develop a Koopman operator model predictive control (KMPC) algorithm. KMPC was compared to a linear time variant (LTV) and a nonlinear model predictive control (NMPC), which are widely used in the literature, and showed better performance in some cases and a reduction in computational complexity in all cases.