Abstract The operating point at which a plant (or process) can provide the best output of a quality criterion associated with this plant may be determined and maintained by a hill-climbing regulator (extremum control system) regardless of normal or unpredictable variations in plant characteristics and exterior perturbations. The controller described in this article is simple in farm, but it is rapid, stable, and capable of high precision. The attractive performance of the regulator results from the use of readily available a priori information, such as the dynamics of the plant and the shape of the non-linear and extremal characteristic representing the quality criterion. The algorithm used to effect control is based on the premise that the shape of the curve of the plant output versus input (extremal characteristic) can nearly always be approximated by a parabola. Therefore, by a partial identification of the true characteristic's shape in the vicinity of the actual operating point, it is possible to predict the approximate location of the characteristic's extremum by performing a parabolic extrapolation of the measured shape from the actual operating point to the presumed optimal operating point. The hill-climbing controller makes use of a deliberate, stepwise variation of the input variable so as to determine the transient change in the output ; the effects of these changes are interpreted by the controller so as to maintain the plant at optimal output. The controller remains stable in the presence of rapid drifts of the extremum because of another extrapolation procedure which compensates for the effects of these drifts. The regulator permits also partial compensation of the retarding effects due to the plant dynamics.