Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems
- In this article, we extend the time-domain decomposition method described by Lagnese and Leugering (2003) to semilinear optimal control problems for hyperbolic balance laws with spatio-temporal varying coefficients. We provide the design of the iterative method applied to the global first-order optimality system, prove its convergence, and derive an a posteriori error estimate. The analysis is done entirely on the continuous level. A distinguishing feature of the method is that the decomposed optimality system can be interpreted as an optimality system of a local "virtual" optimal control problem. Thus, the iterative time-domain decomposition of the optimality system can be interpreted as an iterative parallel scheme for virtual optimal control problems on the subintervals. A typical example and further comments are given to show the range of potential applications. Moreover, we provide some numerical experiments to give a first interpretation of the role of the parameters involved in the iterative process.
Author: | Richard Krug, Günter Leugering, Alexander Martin, Martin Schmidt, Dieter Weninger |
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Parent Title (German): | SIAM Journal on Control and Optimization |
Document Type: | Article |
Language: | English |
Date of Publication (online): | 2020/11/29 |
Date of first Publication: | 2020/11/29 |
Release Date: | 2020/11/29 |
Tag: | A posteriori error estimates; Convergence; Optimal control; Semilinear hyperbolic systems; Time-domain decomposition |
Page Number: | 28 |
Institutes: | Friedrich-Alexander-Universität Erlangen-Nürnberg |
Universität Trier | |
Subprojects: | A05 |
B07 | |
B08 | |
Licence (German): | Creative Commons - CC BY - Namensnennung 4.0 International |