• search hit 2 of 386
Back to Result List

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

  • 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.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Martin Gugat, Meizhi Qian, Jan Sokolowski
Document Type:Article
Language:English
Date of Publication (online):2024/06/27
Release Date:2024/07/01
Tag:Network Optimum Design; Optimal Control; Spectral Method; Turnpike Property; Wave Equation
Volume:J. Geom. Anal.
Issue:34
Article Number:273
Page Number:60
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:C03
C05
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International