A method of network design and control for the wave equation. Shape and topology optimization for the turnpike property - Equations aux dérivées partielles Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

A method of network design and control for the wave equation. Shape and topology optimization for the turnpike property

Résumé

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 taking into account the nonhomogeneous final conditions for the velocity of the adjoint state equation. The proof is given with all details and it contains that given in hal-04285637 as a particular case with homogeneous final conditions for the adjoint state. The shape and topology optimization is performed for the network with the shape functional given by the optimality system of 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.
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Dates et versions

hal-04593373 , version 1 (29-05-2024)

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  • HAL Id : hal-04593373 , version 1

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Martin Gugat, Meizhi Qian, Jan Sokolowski. A method of network design and control for the wave equation. Shape and topology optimization for the turnpike property. 2024. ⟨hal-04593373⟩
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