Direct and indirect multiple shooting for parabolic optimal control problems

• Verfasst von: Carraro, Thomas [VerfasserIn]
• Verfasst von: Geiger, Michael [VerfasserIn]
• Titel: Direct and indirect multiple shooting for parabolic optimal control problems
• Verf.angabe: Thomas Carraro, Michael Geiger
• Umfang: 33 S.
• Titel Quelle: Enthalten in: Multiple shooting and time domain decomposition methods
• Jahr Quelle: 2015
• Band/Heft Quelle: (2015), S. 35-67
• ISBN Quelle: 978-3-319-23320-8
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als Online-Ausgabe: Carraro, Thomas: Direct and indirect multiple shooting for parabolic optimal control problems
• K10plus-PPN: 1563024691

Abstract

We present two multiple shooting approaches for optimal control problems (OCP) governed by parabolic partial differential equations (PDE). In the context of ordinary differential equations, shooting techniques have become a state-of-the-art solver component, whereas their application in the PDE case is still in an early phase of development. We derive both direct (DMS) and indirect (IMS) multiple shooting for PDE optimal control from the same extended problem formulation. This approach shows that they are algebraically equivalent on an abstract function space level. However, discussing their respective algorithmic realizations, we underline differences between DMS and IMS. In the numerical examples, we cover both linear and nonlinear parabolic side conditions.