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Optimal control of a rate-independent system constrained to parameterized balanced viscosity solutions

Thomas, Stephanie

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.

Sponsor
Die Forschung wurde im Rahmen des DFG SPP 1962 gefördert.
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@phdthesis{doi:10.17170/kobra-202205216215,
  author    ={Thomas, Stephanie},
  title    ={Optimal control of a rate-independent  system constrained to parameterized balanced  viscosity solutions},
  keywords ={510 and Optimale Kontrolle and Problem and Optimierung and Viskositätslösung},
  copyright  ={http://creativecommons.org/licenses/by-nc/4.0/},
  language ={en},
  school={Kassel, Universität Kassel, Fachbereich Mathematik und Naturwissenschaften, Institut für Mathematik},
  year   ={2022}
}