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Random disturbance input is bound to cause a state uncertainty. In particular, when the random disturbance input is time correlated, the impact on the state uncertainty becomes more severe. Time correlation, which could also be expressed in terms of an interstage correlation, implies that the value of a one time instant is correlated with the value of another time instant; it suggests that the random disturbance is nonwhite. A run-out-table cooling is a complex dynamic multistage process with intrinsic characteristics such as, long time delay and time-correlated disturbance, therefore it constitutes an exceptional case to investigate stochastic optimization methods, in order to optimally track the temperature trajectory along its stages. Stochastic optimization is applied on an augmented state model, which is a combination of a dynamic disturbance model and the system equation. The merit of the optimal solutions obtained by this approach is confirmed by simulation experiments. The results demonstrate the state propagation and robust tracking performance in the presence of stochastic time-correlated disturbance inputs.