A control apparatus is used for a power-supply apparatus with power-supply systems connected in parallel between a pair of power wires connected to a load. Each power-supply system has a series circuit of a battery and a contact of a relay. When the control apparatus determines that at least one relay suffers from a contact welding, the control apparatus performs a battery charge/discharge process to charge/discharge the batteries through the pair of power wires by turning ON one of possible relays while turning OFF the others of the possible relays. The possible relay is defined as having a possibility of suffering from the contact welding. After the battery charge/discharge process, the control apparatus identifies which possible relay actually suffers from the contact welding based on a change in a state of the battery connected in series with the contact of each possible relay.