Dissertation
Optimal control of a rate-independent system constrained to parameterized balanced viscosity solutions
Abstract
In this dissertation, we analyze an optimal control problem governed by a rate-independent system in an abstract infinite-dimensional setting. The rate-independent system is characterized by a nonconvex stored energy functional, which depends on time via a time-dependent external loading, and by a convex dissipation potential, which is assumed to be bounded and positively homogeneous of degree one.
The optimal control problem uses the external load as control variable and is constrained to normalized parametrized balanced viscosity solutions (BV solutions) of the rate-independent system. Solutions of this type appear as vanishing viscosity limits of viscously regularized versions of the original rate-independent system. Since BV solutions in general are not unique, as a main ingredient for the existence of optimal solutions we prove the compactness of solution sets for BV solutions.
The optimal control problem uses the external load as control variable and is constrained to normalized parametrized balanced viscosity solutions (BV solutions) of the rate-independent system. Solutions of this type appear as vanishing viscosity limits of viscously regularized versions of the original rate-independent system. Since BV solutions in general are not unique, as a main ingredient for the existence of optimal solutions we prove the compactness of solution sets for BV solutions.
Sponsorship
Die Forschung wurde im Rahmen des DFG SPP 1962 gefördert.Citation
@phdthesis{doi:10.17170/kobra-202205216215,
author={Thomas, Stephanie},
title={Optimal control of a rate-independent system constrained to parameterized balanced viscosity solutions},
school={Kassel, Universität Kassel, Fachbereich Mathematik und Naturwissenschaften, Institut für Mathematik},
year={2022}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2022$n2022 1500 1/eng 2050 ##0##http://hdl.handle.net/123456789/13885 3000 Thomas, Stephanie 4000 Optimal control of a rate-independent system constrained to parameterized balanced viscosity solutions / Thomas, Stephanie 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/http://hdl.handle.net/123456789/13885=x R 4204 \$dDissertation 4170 5550 {{Optimale Kontrolle}} 5550 {{Problem}} 5550 {{Optimierung}} 5550 {{Viskositätslösung}} 7136 ##0##http://hdl.handle.net/123456789/13885
2022-06-01T10:56:33Z 2022-06-01T10:56:33Z 2022 doi:10.17170/kobra-202205216215 http://hdl.handle.net/123456789/13885 Die Forschung wurde im Rahmen des DFG SPP 1962 gefördert. eng Namensnennung-Nicht-kommerziell 4.0 International http://creativecommons.org/licenses/by-nc/4.0/ Optimization Rate-independent systems vanishing viscosity balanced viscosity solutions non-convex 510 Optimal control of a rate-independent system constrained to parameterized balanced viscosity solutions Dissertation In this dissertation, we analyze an optimal control problem governed by a rate-independent system in an abstract infinite-dimensional setting. The rate-independent system is characterized by a nonconvex stored energy functional, which depends on time via a time-dependent external loading, and by a convex dissipation potential, which is assumed to be bounded and positively homogeneous of degree one. The optimal control problem uses the external load as control variable and is constrained to normalized parametrized balanced viscosity solutions (BV solutions) of the rate-independent system. Solutions of this type appear as vanishing viscosity limits of viscously regularized versions of the original rate-independent system. Since BV solutions in general are not unique, as a main ingredient for the existence of optimal solutions we prove the compactness of solution sets for BV solutions. open access Thomas, Stephanie 2022-04-25 x, 11-162 Seiten Kassel, Universität Kassel, Fachbereich Mathematik und Naturwissenschaften, Institut für Mathematik Knees, Dorothee (Prof. Dr.) Meyer, Christian (Prof. Dr.) DFG SPP 1962 Optimale Kontrolle Problem Optimierung Viskositätslösung publishedVersion false true
The following license files are associated with this item: