Coordinated Receding-Horizon Control of Battery Electric Vehicle Speed and Gearshift Using Relaxed Mixed-Integer Nonlinear Programming

In this article, we investigate coordinated receding-horizon control of vehicle speed and transmission gearshift for energy-efficient operation of automated battery electric vehicles (BEVs). The introduction of multispeed transmissions in BEVs enables manipulation of electric motor operating point under given vehicle speed and acceleration command, thus creating the opportunity to further improve BEV energy efficiency. However, co-optimizing vehicle speed and transmission gearshift leads to a mixed-integer nonlinear programming (MINLP) problem, and it is well known that solving MINLP problems is computationally very challenging. To address this challenge, we propose a novel continuous relaxation technique that enables the computation of solutions to the speed and gearshift co-optimization problem using off-the-shelf nonlinear programming solvers. After analyzing theoretical properties of the proposed relaxation technique, we demonstrate its effectiveness through simulation-based case studies, where we show that co-optimizing vehicle speed and transmission gearshift can lead to considerably greater energy efficiency than optimizing them separately or sequentially and the proposed relaxation technique can reduce the computational cost of the co-optimization problem to a level that is comparable to the time budget available for onboard implementation.