An Approximately Optimal Extremul Regulator†

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Abstract
Many chemical and mineral processing plants are extremal systems, that is they have a best control setting from which deviation in any direction lowers the product yield. The model for such systems has u peaked nonlinear characteristic in the output. Previous empirieal controllers have estimated the slope of the characteristic at the current working point, and then adjusted the control for maximum yield. This paper demonstrates the theory of optimal control of extremal systems. Detailed results are given for a one-dimensional model with (i) random fluctuations in the non-linear characteristic, (ii) noise on the output measurements, (iii) noise in the control path, (iv) dynamics in the control path. Only approximate computations are feasible on a small digital computer, the approximation here incorporates certain features of tho empirical method. Comparisons between the empirical and optimal controller are made.

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