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This paper investigates how a control structure tracks a trajectory of multistage dynamic processes optimally in the presence of exogenous linear or nonlinear unknown system disturbances. In accordance with previous work, run-out table temperature control for hot strip cooling (a prime model of metal-cooling multistage process) serves as the basis system. We study optimal solutions in terms of disturbance attenuation of various characteristics with minimal degradation on the performance of the system. Optimization and dynamic programming are instrumental in obtaining meaningful and tractable problem formulations and determining the necessary and sufficient conditions, which lead to optimal and efficient solutions in relation to the presence of the disturbance. The effectiveness of this development is presented in terms of robust system performance and verified by way of simulation.