In this paper we study the optimal redesign of output trajectories for linear invertible systems. This is particularly important for tracking control of flexible structures because the input-state trajectories, that achieve tracking of the required output, may cause excessive vibrations in the structure. Therefore, a trade-off is required between tracking and vibration reduction. We pose and solve this problem, in the context of linear systems, as the minimization of a quadratic cost function. The theory is developed and applied to the output tracking of a flexible structure and experimental results are presented.

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