Abstract
A tracking problem on an infinite time interval is studied, where the plant is linear with quadratic cost, and the tracked trajectory is not necessarily period. Optimal solutions with respect to the overtaking criterion are studied. Existence and uniqueness of such optimal solutions are proved and they are shown to be given by a linear feedback law which is the same as in the periodic case. A close relation between the solutions of tracking problems where the tracked trajectories are different only for very large times is established.
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Leizarowitz, A. Tracking nonperiodic trajectories with the overtaking criterion. Appl Math Optim 14, 155–171 (1986). https://doi.org/10.1007/BF01442233
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DOI: https://doi.org/10.1007/BF01442233