Sufficient Conditions for Speed Optimization Based on Pontryagin’s Minimum Principle in Battery Electric Vehicles

As an optimal control method, Pontryagin’s minimum principle (PMP) can be applied to optimize the speed of battery electric vehicles (BEVs) to reduce energy consumption. However, the necessary conditions of PMP can only provide candidates for a globally optimal solution, and cannot guarantee the global optimality of the optimization results. Few studies have mathematically proven global optimality of the speed optimization problem for BEVs based on PMP. Building on previous studies, the contribution of this study is the proposal of a new approach to prove global optimality of PMP. The innovation lies in proposing an equivalent costate to replace the costate from PMP. In addition, this study also proposes sufficient conditions for global optimality in the speed optimization problem for BEVs based on PMP: motor power is a convex function of the propulsion force on the wheels, and vehicle speed. It is noteworthy that this sufficient condition is independent of the costate. In conclusion, we demonstrate that the solution obtained using PMP is globally optimal for the speed optimization problem of BEVs, provided that the characteristics of the BEVs satisfy the sufficient condition.