Predictive energy management of fuel cell plug-in hybrid electric vehicles: A co-state boundaries-oriented PMP optimization approach

This paper proposes a predictive energy management strategy of FC PHEV based on PMP and co-state boundaries. The model predictive control (MPC) problem is established and transformed as a two-point-boundary-value one by PMP theory, and the physical constraints of FC power, FC power varying rate, and battery current, are merged by methodical derivatives. To gain the accurate co-state boundaries, the Karush-Kuhn-Tucker condition, for the first time, is employed to derive the general expressions, and a correction method is developed to modify the co-state boundaries for effectiveness guarantees. By inputting the feedback SOC, power demand, and the unified constraint, the shrunken enclosed range between the developed co-state boundaries can be determined in real time, thereby benefiting the efficient co-state calibration. Based on the co-state bounds, the concise but highly effective heuristic rules are proposed to calibrate the co-state online iteratively, and an analytical method is proposed to fast find the optimal solution of Hamilton function. The global optimality of the proposed strategy for the addressed MPC problem is also strictly proved. The validations and sensitivity analysis for the initial state of charge (SOC), the SOC reference, the predictive velocity accuracy, and the horizon length, are implemented under simulations, and the hardware-in-the-loop (HIL) experiments are carried out to verify the effectiveness of the proposed strategy under on-board environment. The results yield that, the proposed strategy can implement the timely and high-efficiency co-state updates, the smooth control commands, the expected SOC tracking effects, and improve the fuel economy. Additionally, <0.5 ms per sample is spent for the predictive horizon length 40 under HIL tests, indicating the real-time applicability of proposed strategy.