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1. An on-board control device for application to an on-board system including a power source unit, a power path through which power is supplied from the power source unit, and a plurality of branch paths branching out from the power path, the on-board control device comprising: a plurality of relays, each of the plurality of relays disposed on a corresponding one of the plurality of branch paths; a control unit configured to control the plurality of relays; and a plurality of current detection units, each of the plurality of current detection units disposed on a corresponding one of the plurality of branch paths and configured to detect a value of current flowing through each of the branch paths, the plurality of relays interposed between the power source unit and the plurality of current detection units, wherein the relays each switch between an allowance state of allowing current flow on the respective branch path and a shut off state of shutting off the current flow, when a predetermined anomalous state is detected, the control unit switches the relay provided on a specific branch path on which a current value is increasing at a fastest rate among the plurality of branch paths to the shut off state, based on detection results of the current detection unit, the control unit, furthermore, takes the branch path with respect to which a value obtained by time differentiating the current value is largest as the specific branch path, and switches the relay provided on the specific branch path to the shut off state, and the control unit, furthermore, includes: a determination circuit configured to output an anomaly signal when the anomalous state occurs; a differential circuit configured to time differentiate the current value of each of the branch paths detected by the current detection unit; a selection circuit configured to output a selection signal indicating the branch path with respect to which a largest differential value is obtained among differential values obtained by time differentiating the respective current values, based on calculation results of the differential circuit; and a shut-off circuit configured to switch the relay provided on the branch path indicated by the selection signal to the shut off state, when input of the anomaly signal is received.
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