A Fast Dynamic Programming (FDP) algorithm is proposed to optimize the fuel consumption of the Plug-in Hybrid Electronic Vehicles (PHEV) over a prescribed driving cycle. Firstly, an innovative DP mathematical model for PHEV with reduced dimension is created. It composes of a linear state transfer equation and a quadratic cost function with 1×1 dimension. Based on this model, two algorithms expressed as the simple analytic forms are derived. One is the control algorithm for the optimal power splitting ratio (PSR) between the internal combustion engine (ICE) power and demand power. Another is the recursive algorithm to calculate the optimization value of the fuel consumption. Then, the optimal output power of ICE (or electronic motor (EM)) and the optimal speed ratio of the gear position can be calculated rapidly as the consequence of using the algorithms with analytic forms. Finally, the simulation results confirm that the computational efficiency of the FDP control algorithm has been improved with a geometric ratio, while its control performance maintains in an acceptable range in contrast with conventional DP control algorithm.

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