Model continuity approximations and real-time nonlinear optimization in cost-optimal predictive energy management of fuel cell hybrid electric vehicles

For saving fuel and extending the fuel cells (FC)/battery lifetime, this paper proposes a real-time cost-optimal predictive energy management strategy of FC hybrid electric vehicles based on continuation/general minimal residuals (C/GMRES) algorithm. To ensure the preferable continuation for algorithm application, the continuity method is proposed for accurate model approximations. The external penalty method is employed to transform the inequality constraints as an equivalent index cost. Then, the continuous and unconstrained model predictive control problem is reformulated, and the C/GMRES algorithm is proposed for real-time optimization. Given the output, the expected FC control command can be decided by the designed postprocessing rules. The performance of the proposed strategy is validated under simulations and hardware-in-the-loop (HIL) tests. The results manifest that the proposed strategy can effectively save the total cost for the predictive horizon of 5s-60s even when the neural network-based predictive velocity is adopted. Besides, compared with the interior point method, the proposed C/GMRES algorithm achieves similar solving effects while exhibiting more than 100 times computing efficiency. In addition, the execution time of the proposed strategy in each step is less than 1.2 ms under HIL tests, indicating its real-time applicability.