  In this paper, we propose an approach to coordinated receding-horizon control
of vehicle speed and transmission gearshift for automated battery electric
vehicles (BEVs) to achieve improved energy efficiency. The introduction of
multi-speed transmissions in BEVs creates an opportunity to manipulate the
operating point of electric motors under given vehicle speed and acceleration
command, thus providing the potential to further improve the energy efficiency.
However, co-optimization of vehicle speed and transmission gearshift leads to a
mixed integer nonlinear program (MINLP), solving which can be computationally
very challenging. In this paper, we propose a novel continuous relaxation
technique to treat such MINLPs that makes it possible to compute solutions with
conventional nonlinear programming solvers. After analyzing its theoretical
properties, we use it to solve the optimization problem involved in coordinated
receding-horizon control of BEV speed and gearshift. Through simulation
studies, we show that co-optimizing vehicle speed and transmission gearshift
can achieve considerably greater energy efficiency than optimizing them
sequentially, and the proposed relaxation technique can reduce the online
computational cost to a level that is comparable to the time available for
real-time implementation.
