A jump condition of PMP-based control for PHEVs

An optimal control strategy based on Pontryagin's Minimum Principle (PMP) is a promising solution because it provides a simple solution for controlling Hybrid Electric Vehicles (HEVs) and guarantees the best performance under reasonable conditions [1] and [2]. However, it needs to be very careful when applying the control strategy if inequality state constraints are active because handling the state constraints is one of the difficult issues in optimal control problems. In contrast to HEVs, Plug-in Hybrid Electric Vehicles (PHEVs) possibly consume all of the available electric energy, and so the activation of the state constraint on minimum State of Charge (SOC) is, unfortunately, a very common control problem for PHEVs. This paper describes mathematical derivations for an additional condition necessary for the inequality state constraints and solves the problem with several control options. Whereas PMP-based control allows a unique solution for HEVs [2], this paper shows that the control idea based on PMP produces a number of alternative solutions for PHEVs. However, battery efficiencies can be considered to evaluate the optimality of each solution, and simulation results from several control options show that maximizing a blended-mode control is the best solution to saving fuel for PHEVs. In terms of performance, the results of applying blended-mode control are very close to those obtained by applying a global optimal solution obtained from Dynamic Programming (DP).

► We derive a jump condition when PMP-based control for PHEVs includes state inequality constraints.
► Based on the jump condition, we could obtain several control solutions that satisfy the necessary condition of PMP.
► Considering the battery characteristic, we conclude that maximizing blended mode could be the best solution.
► Numerical simulation proves that the solution, maximizing blended mode, is superior to other control solutions.