Sufficient conditions of optimal control based on Pontryagin’s minimum principle for use in hybrid electric vehicles

Over 10 years ago, the equivalent consumption minimization strategy was introduced as an effective approach, using the concept of equivalent fuel consumption for electricity use, to solve a control problem for hybrid electric vehicles. Although numerous studies have documented outstanding results as a consequence of applying the concept and have shown that the equivalent consumption minimization strategy could be explained on the basis of an optimal control concept such as Pontryagin’s minimum principle, few studies have proven, mathematically, its optimal performance when solving the control problem of hybrid electric vehicles. The present research builds upon previous research studies that proved that the control based on Pontryagin’s minimum principle can be a global optimal solution for hybrid electric vehicles under the assumption that the battery efficiency is not a function of the state of charge. In this paper, we expand upon the original concept, deriving the optimality within more generalized cases than previously reported. In conclusion, if the battery efficiency is a concave function of the state of charge, which is possibly a natural characteristic of the battery, the optimal control based on Pontryagin’s minimum principle enables optimal performance to be achieved. We can therefore apply this control concept to hybrid electric vehicles which use a wide range of states of charge, such as plug-in hybrid electric vehicles.