In a system for controlling a plant (engine) 10 having an input u, there are provided with applying device (vibration signal) 100 for applying a component p that changes at a predetermined cycle to the plant, parameter calculating device (Washout Filter) 102 for calculating a parameter h based on an output y of the plant, integrating device (finite interval integrator) 104 for integrating a value j obtained by multiplying the calculated parameter h by the applied component p in an interval of integral multiple of a cycle of the component p, and input calculating devices (infinite interval integrator 106a, multiplier 106b, adder 106c) for calculating the input u based on the integrated value g obtained by the integration. Owing to this configuration, it becomes possible to provide a system that can optimize the output y, while preventing the resonance of the control system while, thereby enabling to control the output of the plant to the extremum point.