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This paper presents an approach to the problem of controlling the electricity generation of series hybrid electric vehicles (SHEVs) and proposes an algorithm with the goal to minimize fuel consumption. Starting from the knowledge of the vehicle electric generator consumption maps, as well as information on the vehicle battery behavior, and on some overall parameters characterizing the expected trip, the algorithm is able to define: whether to continuously keep the generator in the ON state or not; when to, if is the case, switch the generator ON or OFF; the instantaneous power to be delivered by the electric generator when in ON state. Adopting such parameters enables avoiding to previously know the battery losses on a given trip and offers the possibility to update the control according to online measures. Addresses are also given on how to online assess the trip parameters to be used as inputs for the algorithm.