Turnpike properties of optimal boundary control problems with random linear hyperbolic systems

Gugat M, Herty M (2023)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2023

Journal

Esaim-Control Optimisation and Calculus of Variations EDP Sciences

Book Volume: 29

Article Number: 55

URI: https://www.esaim-cocv.org/articles/cocv/abs/2023/01/cocv220028/cocv220028.html

DOI: 10.1051/cocv/2023051

Open Access Link: https://www.esaim-cocv.org/articles/cocv/abs/2023/01/cocv220028/cocv220028.html

Abstract

In many applications, in systems that are governed by linear hyperbolic partial differential equations some of the problem parameters are uncertain. If information about the probability distribution of the parametric uncertainty, distribution is available, the uncertain state of the system can be described using an intrinsic formulation through a polynomial chaos expansion. This allows to obtain solutions for optimal boundary control problems with random parameters. We show that similar to the deterministic case, a turnpike result holds in the sense that for large time horizons the optimal states for dynamic optimal control problems on a substantial part of the time interval approaches the optimal states for the corresponding uncertain static optimal control problem. We show turnpike results both for the full uncertain system as well as for a generalized polynomial chaos approximation.

Authors with CRIS profile

Martin Gugat Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen DE Germany (DE)

How to cite

APA:

Gugat, M., & Herty, M. (2023). Turnpike properties of optimal boundary control problems with random linear hyperbolic systems. Esaim-Control Optimisation and Calculus of Variations, 29. https://doi.org/10.1051/cocv/2023051

MLA:

Gugat, Martin, and Michael Herty. "Turnpike properties of optimal boundary control problems with random linear hyperbolic systems." Esaim-Control Optimisation and Calculus of Variations 29 (2023).

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