Some Statistical Aspects of Adaptive Optimization and Control

It is often necessary to adjust some variable X such as the concentration of consecutive batches of a product, to keep X close to a specified target value. A second more complicated problem occurs when the independent variables X in a response function η(X) are to be adjusted so that the derivatives ∂η/∂Xare kept close to a target value zero, thus maximizing or minimizing the response. These are shown to be problems of prediction, essentially, and the paper is devoted mainly to the estimation from past data of the “best” adjustments to be applied in the first problem.