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Pré-Publication, Document De Travail Année : 2022

An aspect of the turnpike property. Long time horizon behavior

Résumé

The turnpike phenomenon concerns the structure of optimal controls and the optimal state of dynamic optimal control problems for long time horizons. The focus is regularly on the study of the interior of the time interval. Classical turnpike results state how the solution of the dynamic optimal control problems approaches the solution of the corresponding static optimal control problem in the interior of the time interval. In this paper we look at a new aspect of the turnpike phenomenon. We show that for problems without explicit terminal condition, for large time horizons in the last part of the time interval for large T the optimal state approaches a certain limit trajectory that is independent of the terminal time exponentially fast. Similarly also in the initial part of the time interval for large T the optimal state approaches a certain limit state exponentially fast.
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Dates et versions

hal-03780440 , version 1 (19-09-2022)

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  • HAL Id : hal-03780440 , version 1

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Martin Gugat, Jan Sokolowski. An aspect of the turnpike property. Long time horizon behavior. 2022. ⟨hal-03780440⟩
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