A controller for a plant that controls a controlled variable for the plant in accordance with estimated values, allowing to reduce any error in the estimated values that is caused by solid variation or aging of the plant. A controller for an exhaust emission control system has an estimated Inert-EGR value calculation section (711) to calculate the estimated value IEGRHAT for the Inert-EGR amount on the basis of an input vector U through a neural network, an estimated LAF sensor output value calculation section (712) to calculate the estimated value ΦHAT for an exhaust air-fuel ratio correlating with the Inert-EGR amount on the basis of the input vector U through the neural network, an LAF sensor (34) to detect the exhaust air-fuel ratio, and a nonlinear adaptive corrector (713) to calculate the adaptive input UVNS such that the estimated error EHAT between the detected value ΦACT from the LAF sensor (34) and the estimated output value ΦHAT of the LAF sensor (34) is minimized.