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A Turnpike Result for Optimal Boundary Control Problems with the Transport Equation under Uncertainty

Submission Status:under review
  • In this paper we analyze the turnpike phenomenon for optimal boundary control problems with a linear transport equation with source term. The convex objective function depends on the boundary traces of the transport equation and is strictly convex with respect to the boundary control. We show an integral turnpike result for an optimal Dirichlet boundary control problem in the sense that if the time horizon goes to infinity, then the dynamic optimal control converges to the corresponding steady state optimal control. The novelty of this work is two-sided. On the one hand, even if turnpike results for this kind of optimal boundary control problem already exist, we present a new direct proof without using adjoint calculus that leads to sharper estimates. On the other hand we consider uncertainty in the initial data and/or in the source term. We show that the integral turnpike result also holds considering uncertainty. Throughout the paper we use numerical examples to illustrate the results.

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Author:Michael Schuster, Noboru Sakamoto
Document Type:Preprint
Language:English
Date of Publication (online):2023/03/14
Release Date:2023/03/14
Tag:Boundary Control; Random Boundary Data; Transport Equation; Turnpike
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:C03
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International