  Nonlinear dynamics bring difficulties to controller design for control-affine
systems such as tractor-trailer vehicles, especially when the parameters in the
dynamics are unknown. To address this constraint, we propose a derivative-based
lifting function construction method, show that the corresponding infinite
dimensional Koopman bilinear model over the lifting function is equivalent to
the original control-affine system. Further, we analyze the propagation and
bounds of state prediction errors caused by the truncation in derivative order.
The identified finite dimensional Koopman bilinear model would serve as
predictive model in the next step. Koopman Bilinear Model Predictive control
(K-BMPC) is proposed to solve the trajectory tracking problem. We linearize the
bilinear model around the estimation of the lifted state and control input.
Then the bilinear Model Predictive Control problem is approximated by a
quadratic programming problem. Further, the estimation is updated at each
iteration until the convergence is reached. Moreover, we implement our
algorithm on a tractor-trailer system, taking into account the longitudinal and
side slip effects. The open-loop simulation shows the proposed Koopman bilinear
model captures the dynamics with unknown parameters and has good prediction
performance. Closed-loop tracking results show the proposed K-BMPC exhibits
elevated tracking precision with the commendable computational efficiency. The
experimental results demonstrate the feasibility of K-BMPC.
