Comparative study of dynamic programming and pontryagin's minimum principle on energy management for a parallel hybrid electric vehicle

This paper compares two optimal energy management methods for parallel hybrid electric vehicles using an Automatic Manual Transmission (AMT). A control-oriented model of the powertrain and vehicle dynamics is built first. The energy management is formulated as a typical optimal control problem to trade off the fuel consumption and gear shifting frequency under admissible constraints. The Dynamic Programming (DP) and Pontryagin's Minimum Principle (PMP) are applied to obtain the optimal solutions. Tuning with the appropriate co-states, the PMP solution is found to be very close to that from DP. The solution for the gear shifting in PMP has an algebraic expression associated with the vehicular velocity and can be implemented more efficiently in the control algorithm. The computation time of PMP is significantly less than DP.