Robustification Through Minimax Dynamic Programing and Its Implication for Hybrid Vehicle Energy Management Strategies

Hybrid electric vehicle (HEV) control strategies are often designed around specific driving conditions. However, when driving conditions differ from the designed conditions, HEV performance can suffer. This paper develops a novel HEV energy management strategy (EMS) that is robust to uncertain driving conditions by augmenting a stochastic dynamic programing (SDP) controller with minimax dynamic programing (MDP). This combination of MDP and SDP has not previously been studied in the literature. The stochastic element uses a Markov chain model to represent driver behavior and is used to optimize the control for expected future driver behavior. The minimax element instead optimizes against potential worst-case (maximal cost) future driver behavior. The resulting EMS can be directly implemented on a vehicle. This method is demonstrated on a series hybrid electric bus model. Robustness to uncertain driving conditions is tested by simulating on a variety of heavy-duty vehicle drive cycles that differ from the drive cycle on which the EMS was trained. A single tuning parameter is used to balance the stochastic and minimax elements of the EMS, and a parametric study shows the effects of this tuning parameter. It was found that using minimax control could increase the vehicle fuel economy on multiple uncertain driving conditions, with a tradeoff of decreased fuel economy when the driving conditions match the designed conditions. That is, it offers an exchange of performance on the nominal driving conditions for performance on uncertain driving conditions.