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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.

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Verfasserangaben:Richard Krug, Günter Leugering, Alexander Martin, Martin Schmidt, Dieter Weninger
Titel des übergeordneten Werkes (Deutsch):SIAM Journal on Control and Optimization
Dokumentart:Wissenschaftlicher Artikel
Sprache:Englisch
Datum der Veröffentlichung (online):29.11.2020
Datum der Erstveröffentlichung:29.11.2020
Datum der Freischaltung:29.11.2020
Freies Schlagwort / Tag:A posteriori error estimates; Convergence; Optimal control; Semilinear hyperbolic systems; Time-domain decomposition
Seitenzahl:28
Institute:Friedrich-Alexander-Universität Erlangen-Nürnberg
Universität Trier
Teilprojekte:A05
B07
B08
Lizenz (Deutsch):License LogoCreative Commons - CC BY - Namensnennung 4.0 International