A control apparatus controls an inverter (electric power converter circuit) which is connected for selectively applying a plurality of voltage levels to each phase of a polyphase rotary machine. In each of successive control periods, the apparatus determines the inverter operation state (combination of respective voltage levels applied to the phases) to be set for the succeeding control period, by performing prediction calculations based on a model of the rotary machine, for each of a plurality of candidates for the next operation state, to select an optimum candidate. The candidates are restricted to those operation states whereby the voltage level of no more than one of the phases will be changed, at changeover to the operation state of the next control period.