OPTIMAL CONTROL WHEN THE VARIANCE OF THE MANIPULATED VARIABLE IS CONSTRAINED.

Discrete feedback control schemes discussed by Box and Jenkins were designed to produce minimum mean square error in the output. It was tacitly supposed that there was no restriction in the degree of manipulation that could be applied to x sub t the input or manipulated variable to achieve this. It sometimes happens that we are not able to employ these optimal schemes because the amount of variation which can be allowed in the input adjustments x sub t is restricted by practical limitations. It is considered, therefore, how the previous control schemes would need to be modified if a constraint was placed on Vx sub t the variance in the input. Such modified schemes are of considerable practical importance because unrestricted schemes can call for excessively large values of Vx sub t.