Sufficient conditions for optimal energy management strategies of fuel cell hybrid electric vehicles based on Pontryagin's minimum principle

Although an onboard fuel cell system is able to provide sufficient electricity to power a vehicle, a secondary energy storage system such as an electrical battery is desirable because the fuel cell system is generally not capable of braking energy recuperation, and the efficiency of the fuel cell system can be improved by using the secondary energy system. In this paper, sufficient conditions are obtained for an optimal control idea for fuel cell hybrid electric vehicles when the fuel cell system is combined with a rechargeable battery. The optimal control is based on Pontryagin's minimum principle, and this study demonstrates that it results in total hydrogen consumptions if the properties of the fuel cell hybrid system satisfy two assumptions: first, the hydrogen consumption rate of the fuel cell system is convex and, second, the time derivative of the state of charge is concave. In order to validate optimality of the control concept, a vehicle simulation model is developed for a fuel cell hybrid electric vehicle, and control based on Pontryagin's minimum principle is applied in a backward-looking simulator. In the simulation results, control based on Pontryagin's minimum principle produces an optimal solution, which is very close to the global optimal solution obtained by dynamic programming. In addition, control based on Pontryagin's minimum principle simplifies the control organization; the control concept should be considered as a promising solution for fuel cell hybrid electric vehicles because it really achieves results which are near the global optimal results