@incollection{WenzkeLykinaPickenhain, author = {Wenzke, Diana and Lykina, Valeriya and Pickenhain, Sabine}, title = {State and Time Transformations of Infinite Horizon Optimal Control Problems}, series = {Variational and Optimal Control Problems on Unbounded Domains (AMS)}, booktitle = {Variational and Optimal Control Problems on Unbounded Domains (AMS)}, publisher = {American Mathematical Society (AMS)}, address = {Providence, RI}, isbn = {978-1-4704-1077-3}, pages = {189 -- 208}, language = {en} } @techreport{WenzkePickenhain, author = {Wenzke, Diana and Pickenhain, Sabine}, title = {Transformation of Infinite Horizon Optimal Control Problems}, publisher = {Mathematisches Institut}, address = {Cottbus}, pages = {16 Blatt}, abstract = {We consider classes of infinite horizon optimal control problems as optimization problems in Hilbert spaces. For typical examples it is pointed out that the state and control variables belong to Weighted Sobolev - and Lebesgue spaces respectively. The main purpose of this paper is to demonstrate that necessary optimality conditions as the core relation,[1], or a Pontryagin type Maximum Principle including transversality conditions,[19], depend on transformations. Firstly, it is shown that a discount rate can be generated by a transformation. Secondly,a transformation of the infinite horizon problem onto a finite fixed horizon problem generates singularities in the data of the problems or in the optimal solution. Thus standard existence results and necessary optimality conditions,[10], can not be applied for the transformed problem. But results obtained for the infinite horizon problem can be transformed into these for the finite horizon problem.}, language = {en} }