Sensitivity analysis for assessing robustness of position- based predictive energy management strategy for fuel cell hybrid electric vehicle

Under hilly road conditions, it is difficult to achieve near-optimal performance of energy management strategy (EMS) of fuel cell hybrid electric vehicle (FCHEV). In order to achieve near-optimality, optimal state reference trajectory is predicted based on future information, and thus reference tracking controller is often considered as real-time predictive EMS. There are two approaches depending on in what way the predicted reference will be used as follows: 1) position-based predictive EMS for tracking positiondependent reference, 2) time-based predictive EMS for tracking time-dependent reference. In this paper, analytical sensitivity analysis based on Pontryagin’s minimum principle (PMP) is performed to prove robustness of position-based predictive EMS with respect to velocity uncertainty. First, optimal control problem is formulated in time and position domain, and PMP approach is used to derive boundary value problem (BVP) that achieves global optimality. Then, sensitivity differential equations are developed which describe sensitivity of original BVP with respect to velocity uncertainty. Finally, these equations will be solved simultaneously with the original BVP to compute first-order sensitivity of timeand positiondependent optimal state. Results show that sensitivity of time-dependent optimal state is much bigger than that of position-dependent optimal state because velocity uncertainty can change predicted travel time, and this effect on sensitivity is significant. Therefore, predictive EMS should use current position to track position-dependent optimal state reference in terms of the robustness with respect to velocity uncertainty.