Extremum Control in the Presence of Noise†

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Abstract
An extremum control system is considered in which the output from a plant is minimized by adjusting inputs to the plant in discrete steps of constant size. The direction of stepping is determined by estimates of the true output in the presence of Gaussian noise. The criterion of steady-state performance is the average deviation of the true output from the minimum. Performance of a system with single-input plant is computed when one estimate of output is made after each step; the analysis is supported by experimental results. Analysis is simpler when two independent estimates are made per step; performances of the two types of system are compared. Limiting results for vanishing step size in the two-estimate system are derived for a single-input plant with both output noise and input disturbance, and for a multi-input plant with output noise only.

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