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This paper addresses the active control of a hybrid energy storage device, comprised of both battery and ultracapacitor cells embedded in a full electric shuttle. To distribute the power flows within the energy storage device, two criteria are under study, namely battery stress and global heat release minimization, and they are showed to be antagonistic. The optimization is carried out offline via the optimal control theory, and online thanks to heuristics designed to mimic the optimal policy. For each criterion, both approaches are compared through simulation results.