A controller for controlling a plant comprises a predictor for calculating a predicted value of the future of a control output value based on a provisional value of a control input value including a periodic reference signal by using a plant model indicating the dynamic characteristics of the control output value from the control input value of the plant, an evaluation function value calculator for calculating an evaluation function value including the predicted value of the future of the calculated control output value, an extreme value search optimizer for calculating a provisional value of such a control input value as that the evaluation function value becomes the extreme value on the basis of a product of the calculated evaluation function value and a periodic reference signal, and an adder for calculating a control input value including the provisional value of the calculated control input value.