What is it about?
In optimal control of dynamic system, the shape of the domain can be considered as a design variable. This leads to a problem of shape optimization. The turnpike property that we show holds uniformly with respect to shape in this situation is a rational to replace the dynamic problem by the static optimal design problem, which can be solved more efficiently.
Featured Image
Photo by JJ Ying on Unsplash
Why is it important?
Shape optimization is famous for its computational complexity. While many applications require shape optimization for transient systems, often only solutions of the static shape optimization problem are in computational reach. Our contribution give a justification of this reduction and explains why it yields results that are also useful for the transient case.
Perspectives
We are convinced that our result also holds for dynamic optimal control problems in elasticity.
Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Read the Original
This page is a summary of: Network Design and Control: Shape and Topology Optimization for the Turnpike Property for the Wave Equation, Journal of Geometric Analysis, June 2024, Springer Science + Business Media,
DOI: 10.1007/s12220-024-01712-8.
You can read the full text:
Contributors
The following have contributed to this page
