Abstract

We consider systems that are governed by linear time-discrete dynamics with an initial condition and a terminal condition for the expected values. We study optimal control problems where in the objective function a term of tracking type for the expected values and a control cost appear. In addition, the feasible states have to satisfy a conservative probabilistic constraint that requires that the probability that the trajectories remain in a given set F is greater than or equal to a given lower bound. An application are optimal control problems related to storage management systems with uncertain in- and output. We give sufficient conditions that imply that the optimal expected trajectories remain close to a certain state that can be characterized as the solution of an optimal control problem without prescribed initial- and terminal condition. In this way we contribute to the study of the turnpike phenomenon that is well-known in mathematical economics and make a step towards the extension of the turnpike theory to problems with probabilistic constraints.

Author information

Contact details are reproduced from the original publication and may be historical.

Martin Gugat

Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

martin.gugat@fau.de

Keywords

  • Probabilistic constraints
  • chance constraints
  • probabilistic robustness
  • here-and-now-decision
  • turnpike phenomenon
  • turnpike result
  • terminal constraint
  • probabilistic turnpike

Mathematics Subject Classification

90C20, 90C31

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Suggested citation

M. Gugat, H. Heitsch, R. Henrion. “A Turnpike Property for Optimal Control Problems with Dynamic Probabilistic Constraints.” Journal of Convex Analysis 30 (2023), No. 3, 1025–1052. https://doi.org/10.68381/jca30047

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Published by Heldermann Verlag, 2023. Rights now held by Banach Press.