Premium
Multiple shooting methods for parabolic optimal control problems with control constraints
Author(s) -
Carraro Thomas,
Geiger Michael
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510294
Subject(s) - optimal control , context (archaeology) , partial differential equation , shooting method , solver , ordinary differential equation , cover (algebra) , mathematics , parabolic partial differential equation , nonlinear system , control (management) , mathematical optimization , computer science , differential equation , mathematical analysis , engineering , physics , artificial intelligence , biology , mechanical engineering , paleontology , quantum mechanics , boundary value problem
In the context of ordinary differential equations, shooting techniques are a state‐of‐the‐art solver component, whereas their application in the framework of partial differential equations (PDE) is still at an early stage. We present two multiple shooting approaches for optimal control problems (OCP) governed by parabolic PDE. Direct and indirect shooting for PDE optimal control stem from the same extended problem formulation. Our approach reveals that they are structurally similar but show major differences in their algorithmic realizations. In the presented numerical examples we cover a nonlinear parabolic optimal control problem with additional control constraints. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)