A direct adaptive rapid tracking methodology for tracking complex trajectories in short-duration, linear, possibly slowly varying, and/or imprecisely known, industrial processes is proposed. The rapid tracking is accomplished by injecting a supplemental control signal to the input of the plant. The direct adaptive control scheme adapts the stabilizing controller to that which will yield fast convergence of the supplemental control learning process. The complete controlled system is capable of tracking closely very complex short reference trajectories, even in the presence of plant input limitations (saturation).

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