Network Design and Control: Shape and Topology Optimization for the Turnpike Property for the Wave Equation

Gugat M, Sokolowski J, Sokolowski J, Qian M (2024)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2024

Journal

Journal of Geometric Analysis Springer Verlag (Germany)

Book Volume: 34

Article Number: 273

URI: https://link.springer.com/article/10.1007/s12220-024-01712-8

DOI: 10.1007/s12220-024-01712-8

Open Access Link: https://link.springer.com/article/10.1007/s12220-024-01712-8

Abstract

The optimal control problems for the wave equation are considered on networks. The turnpike property is shown for the state equation, the adjoint state equation as well as the optimal cost. The shape and topology optimization is performed for the network with the shape functional given by the optimality system of the control problem. The set of admissible shapes for the network is compact in finite dimensions, thus the use of turnpike property is straightforward. The topology optimization is analysed for an example of nucleation of a small cycle at the internal node of network. The topological derivative of the cost is introduced and evaluated in the framework of domain decomposition technique. Numerical examples are provided.

Authors with CRIS profile

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

Related research project(s)

Nodal control and the turnpike phenomenon (DFG/TRR 154 C03) TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154) June 1, 2018 - May 31, 2022

Involved external institutions

Polska Akademia Nauk (PAN) / Polish Academy of Sciences PL Poland (PL) East China Normal University (ECNU) / 华东师范大学 CN China (CN)

How to cite

APA:

Gugat, M., Sokolowski, J., Sokolowski, J., & Qian, M. (2024). Network Design and Control: Shape and Topology Optimization for the Turnpike Property for the Wave Equation. Journal of Geometric Analysis, 34. https://doi.org/10.1007/s12220-024-01712-8

MLA:

Gugat, Martin, et al. "Network Design and Control: Shape and Topology Optimization for the Turnpike Property for the Wave Equation." Journal of Geometric Analysis 34 (2024).

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