Vexler, Boris (Prof. Dr.); Kunisch, Karl (Prof. Dr.); Wachsmuth, Daniel (Prof. Dr.)
Language:
en
Subject group:
MAT Mathematik
TUM classification:
MAT 496d
Abstract:
This thesis is concerned with the analysis of finite element discretizations for time-optimal control problems subject to linear parabolic partial differential equations and constraints for the state evaluated at the free end time. Necessary and sufficient optimality conditions are provided for the regular case and the case of bang-bang controls. A priori discretization error estimates are proved for different control discretization strategies. Efficient algorithms for the numerical solution are discussed.
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This thesis is concerned with the analysis of finite element discretizations for time-optimal control problems subject to linear parabolic partial differential equations and constraints for the state evaluated at the free end time. Necessary and sufficient optimality conditions are provided for the regular case and the case of bang-bang controls. A priori discretization error estimates are proved for different control discretization strategies. Efficient algorithms for the numerical solution are...
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Translated abstract:
Diese Arbeit befasst sich mit der Analyse finiter Elemente Diskretisierungen zeitoptimaler Steuerungsprobleme mit linearer, parabolischer, partieller Differentialgleichung und Zustandsrestriktionen am freien Endzeitpunkt. Notwendige und hinreichende Optimalitätsbedingungen werden für den regulären und den bang-bang Fall untersucht. A priori Fehlerabschätzungen für verschiedene Diskretisierungen der Kontrolle werden bewiesen. Effiziente Algorithmen für die numerische Lösung werden diskutiert.