What is it about?
Turnpike results relate solutions of dynamic optimal control problems to solutions of the corresponding static problems for large time horizons. The optimal control trajectory is decomposed into a transient initial phase of limited length, an intermediate static phase and a transient terminal phase that is again of limited length. The length of the static phase becomes arbitrarily large with growing time horizon. In this paper we show that the initial trajectories and the terminal trajectories tend to certain limit trajectories as the time horizon tends to infinity. This also holds for the optimal state and the dual state.
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Why is it important?
Structural a priori information about the optimal controls is not only of mathematical interest, but can also be helpful to safe computational time. For example, in the static intermidate phase time steps can be made very large without loss of accuracy.
Perspectives
In this paper, for the proofs a technical commutativity assumption is used. We think that the result that limit trajectories exist as the time horizon tends to infinity is true in a much more general situation!
Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Read the Original
This page is a summary of: An aspect of the turnpike property. Long time horizon behavior, Serdica Mathematical Journal, November 2023, Institute of Mathematics and Informatics Bulgarian Academy of Sciences,
DOI: 10.55630/serdica.2023.49.127-154.
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