Geodesic
A Turnpike Property for Optimal Control Problems with Dynamic Probabilistic Constraints
Journal of convex analysis, Tome 30 (2023) no. 3, pp. 1025-1052
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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.
Classification : 90C20, 90C31
Mots-clés : Probabilistic constraints, chance constraints, probabilistic robustness, here-and-now-decision, turnpike phenomenon, turnpike result, terminal constraint, probabilistic turnpike 
@article{JCA_2023_30_3_JCA_2023_30_3_a11,
     author = {M. Gugat and H. Heitsch and R. Henrion},
     title = {A {Turnpike} {Property} for {Optimal} {Control} {Problems} with {Dynamic} {Probabilistic} {Constraints}},
     journal = {Journal of convex analysis},
     pages = {1025--1052},
     year = {2023},
     volume = {30},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_3_JCA_2023_30_3_a11/}
}
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M. Gugat; H. Heitsch; R. Henrion. A Turnpike Property for Optimal Control Problems with Dynamic Probabilistic Constraints. Journal of convex analysis, Tome 30 (2023) no. 3, pp. 1025-1052. http://geodesic.mathdoc.fr/item/JCA_2023_30_3_JCA_2023_30_3_a11/