This article considers the optimal extremal control of processes with quadratic performance or cost index, and with random disturbances (with gaussian independent increments) to thu optimum operating point and random (gaussian, independent) errors in measuring the coat index. Five different controller configurations are considered. Optimum parameters (which give least mean square tracking of the process optimum) are found by using digital computer simulations and pattern search in parameter space. A dimensionless parameter which measures the relative influence of errors and disturbances (as defined above) is derived, and design formulae for the parameters of each of the five controllers are found for a wide range of this parameter, including the asymptotic region in which measurement errors became insignificant. These formulae cover all combinations of the parameters of the basic problem except those in which measurement error is extremely dominant.