Optimal control of a rate-independent evolution equation via viscous regularization
- We study the optimal control of a rate-independent system that is driven by a convex quadratic energy. Since the associated solution mapping is non-smooth, the analysis of such control problems is challenging. In order to derive optimality conditions, we study the regularization of the problem via a smoothing of the dissipation potential and via the addition of some viscosity. The resulting regularized optimal control problem is analyzed. By driving the regularization parameter to zero, we obtain a necessary optimality condition for the original, non-smooth problem.
Author: | Ulisse Stefanelli, Daniel WachsmuthORCiD, Gerd WachsmuthORCiD |
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DOI: | https://doi.org/10.3934/dcdss.2017076 |
ISSN: | 1937-1632 |
ISSN: | 1937-1179 |
Title of the source (English): | Discrete and Continuous Dynamical Systems - Series S (DCDS-S) |
Document Type: | Scientific journal article peer-reviewed |
Language: | English |
Year of publication: | 2017 |
Tag: | Rate-independent system; necessary optimality conditions; optimal control |
Volume/Year: | 10 |
Issue number: | 6 |
First Page: | 1467 |
Last Page: | 1485 |
Faculty/Chair: | Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Optimale Steuerung |