@article{MalanowskiMaurerPickenhain, author = {Malanowski, Kazimierz and Maurer, Helmut and Pickenhain, Sabine}, title = {Second-order sufficient conditions for state-constrained optimal control problems}, language = {en} } @article{PickenhainWagner, author = {Pickenhain, Sabine and Wagner, M.}, title = {Pontryagin principle for state-constrained control problems governed by a first-order PDE system}, language = {en} } @incollection{PickenhainWagner, author = {Pickenhain, Sabine and Wagner, M.}, title = {Critical points in relaxed deposit problems}, series = {Calculus of variations and optimal control, Technion 1998, proceedings of the International Conference on the Calculus of Variations and Related Topics, 25 - 31 March, 1998}, booktitle = {Calculus of variations and optimal control, Technion 1998, proceedings of the International Conference on the Calculus of Variations and Related Topics, 25 - 31 March, 1998}, editor = {Ioffe, Alexander}, publisher = {Chapman \& Hall/CRC}, address = {Boca Raton, Fla. [u.a.]}, isbn = {0-8493-0605-1}, pages = {217 -- 236}, language = {en} } @article{MaurerPickenhain, author = {Maurer, Helmut and Pickenhain, Sabine}, title = {Second-order sufficient conditions for control problems with mixed control-state constraints}, language = {en} } @incollection{PickenhainKloetzler, author = {Pickenhain, Sabine and Kl{\"o}tzler, R.}, title = {Pontryagin's maximum principle for multidimensional control problems}, series = {Optimal control, Conference on Optimal Control, held at the Mathematisches Forschungsinstitut of the University of Freiburg}, booktitle = {Optimal control, Conference on Optimal Control, held at the Mathematisches Forschungsinstitut of the University of Freiburg}, editor = {Bulirsch, Roland}, publisher = {Birkh{\"a}user}, address = {Basel [u.a.]}, isbn = {0-8176-2887-8}, pages = {21 -- 30}, language = {en} } @article{PickenhainWagner, author = {Pickenhain, Sabine and Wagner, Marcus}, title = {Piecewise Continuous Controls in Dieudonn{\´e}-Rashevsky Type Problems}, language = {en} } @incollection{PickenhainMalanowskiMaurer, author = {Pickenhain, Sabine and Malanowski, Kazimierz and Maurer, Helmut}, title = {Second order sufficient conditions for optimal control subject to first order state constraints}, series = {Control and boundary analysis}, booktitle = {Control and boundary analysis}, editor = {Cagnol, John}, publisher = {Chapman \& Hall/CRC}, address = {Boca Raton, Fla}, isbn = {978-1-574-44594-7}, pages = {293 -- 304}, language = {en} } @incollection{PickenhainLykina, author = {Pickenhain, Sabine and Lykina, Valeriya}, title = {Sufficiency conditions for infinite horizon optimal control problems}, language = {en} } @article{PickenhainWagner, author = {Pickenhain, Sabine and Wagner, Marcus}, title = {Minimizing sequences in class-qualified deposit problems}, language = {en} } @incollection{Pickenhain, author = {Pickenhain, Sabine}, title = {On infinite horizon optimal control of a Lotka-Voltera-System}, series = {Recent Advances in Optimization and its Applications in Engineering : The 14th Belgian-French-German Conference on Optimization}, booktitle = {Recent Advances in Optimization and its Applications in Engineering : The 14th Belgian-French-German Conference on Optimization}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {978-3-642-12598-0}, pages = {277 -- 286}, language = {en} } @article{Pickenhain, author = {Pickenhain, Sabine}, title = {Duality theory for state-constrained control problems governed by a first order PDE system}, series = {Control and Cybernetics}, volume = {31}, journal = {Control and Cybernetics}, number = {3}, pages = {833 -- 845}, language = {en} } @incollection{PickenhainWagner, author = {Pickenhain, Sabine and Wagner, M.}, title = {Optimal Control Problems with a First Order PDE System - Necessary and Sufficient Optimality Conditions}, series = {Online optimization of large scale systems}, booktitle = {Online optimization of large scale systems}, editor = {Gr{\"o}tschel, Martin}, publisher = {Springer}, address = {Berlin [u.a.]}, isbn = {3-540-42459-8}, pages = {159 -- 172}, language = {en} } @incollection{Pickenhain, author = {Pickenhain, Sabine}, title = {Duality in optimal control with first order differential equations}, series = {Encyclopedia of optimization, Bd. 1}, booktitle = {Encyclopedia of optimization, Bd. 1}, editor = {Floudas, Christodoulos A. and Pardalos, Panos M.}, publisher = {Kluwer}, address = {Dordrecht [u.a.]}, isbn = {0-7923-7029-5}, pages = {472 -- 477}, language = {en} } @inproceedings{PickenhainLykina, author = {Pickenhain, Sabine and Lykina, Valeriya}, title = {Budget-Constrained Infinite horizon Optimal Control Problems with Linear Dynamics}, series = {55th IEEE Conference on Decision and Control, Las Vegas}, booktitle = {55th IEEE Conference on Decision and Control, Las Vegas}, publisher = {IEEE}, address = {Piscataway, NJ}, isbn = {978-1-5090-1837-6}, doi = {10.1109/CDC.2016.7798543}, pages = {1906 -- 1911}, language = {en} } @inproceedings{BurtchenPickenhainMaurer, author = {Burtchen, Angie and Pickenhain, Sabine and Maurer, Helmut}, title = {Numerical Treatment of the Optimal Energy Control Problem of Hybrid Vehicles}, series = {IEEE 55th Conference on Decision and Control (CDC], December 12-14, 2016, Las Vegas}, booktitle = {IEEE 55th Conference on Decision and Control (CDC], December 12-14, 2016, Las Vegas}, isbn = {978-1-5090-1837-6}, doi = {10.1109/CDC.2016.7799409}, pages = {7377 -- 7383}, language = {en} } @incollection{Pickenhain, author = {Pickenhain, Sabine}, title = {W{\"a}lzlagerrollen - L{\"o}cher - Orbiformen}, series = {Heureka heute : Kostproben praxiswirksamer Mathematik}, booktitle = {Heureka heute : Kostproben praxiswirksamer Mathematik}, editor = {Deweß, G{\"u}nter}, publisher = {Teubner}, address = {Stuttgart [u.a.]}, isbn = {3-8154-2071-7}, pages = {122 -- 133}, language = {de} } @misc{PickenhainBurtchen, author = {Pickenhain, Sabine and Burtchen, Angie}, title = {Regulator Problems on Unbounded Domains : Stationarity-Optimal Control-Asymptotic Controllability}, series = {Vietnam Journal of Mathematics}, volume = {46}, journal = {Vietnam Journal of Mathematics}, number = {4}, issn = {2305-2228}, doi = {10.1007/s10013-018-0304-0}, pages = {837 -- 861}, abstract = {In this paper, we consider a class of infinite horizon variational and control problems arising from economics, quantum mechanics, and stabilization. Herein, we assume that the objective is of regulator type. The problem setting implies a weighted Sobolev space as the state space. For this class of problems, we establish necessary optimality conditions in a form of a Pontryagin type maximum principle. A duality concept of convex analysis is provided and used to find sufficient optimality conditions and to motivate a dual approximation scheme. We apply the theoretical results to find an asymptotically stabilizing control for a linearized Lotka-Volterra type system.}, language = {en} } @techreport{PickenhainLykina, author = {Pickenhain, Sabine and Lykina, Valeriya}, title = {Pontryagin Type Maximum Principle for Budget-Constrained Infinite Horizon Optimal Control Problems with Linear Dynamics}, publisher = {Brandenburgische Technische Universit{\"a}t, Mathematisches Institut}, address = {Cottbus-Senftenberg}, pages = {22}, abstract = {In this paper a class of infinite horizon optimal control problems with an isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamic is allowed. The problem setting includes a weighted Sobolev space as the state space. For this class of problems, we establish the necessary optimality conditions in form of a Pontryagin Type Maximum Principle including a transversality condition. The proved theoretical result is applied to a linear-quadratic regulator problem.}, language = {en} } @misc{Pickenhain, author = {Pickenhain, Sabine}, title = {Infinite Horizon Optimal Control Problems in the Light of Convex Analysis in Hilbert Spaces}, series = {Set-Valued and Variational Analysis}, volume = {23}, journal = {Set-Valued and Variational Analysis}, number = {1}, issn = {1877-0533}, doi = {10.1007/s11228-014-0304-5}, pages = {169 -- 189}, abstract = {In this paper a class of linear-quadratic infinite horizon optimal control problems is considered. Problems of this type are not only of practical interest. They also appear as an approximation of nonlinear problems. The key idea is to introduce weighted Sobolev spaces as state space and weighted Lebesgue spaces as control spaces into the problem setting. We investigate the question of existence of an optimal solution in these spaces and establish a Pontryagin type Maximum Principle as a necessary optimality condition including transversality conditions.}, language = {en} } @techreport{Pickenhain, author = {Pickenhain, Sabine}, title = {Infinite Horizon Problems in the Calculus of Variations - The Role of Transformations with an Application to the Brachistochrone Problem}, publisher = {Brandenburgische Technische Universit{\"a}t, Mathematisches Institut}, address = {Cottbus ; Senftenberg}, pages = {24}, abstract = {In this paper we consider a class of infinite horizon variational problems resulting from a transformation of singular variational problems. Herein we assume that the objective is convex. The problem setting implies a weighted Sobolev space as state space. For this class of problems we establish necessary optimality conditions in form of a Pontryagin type maximum principle. A duality concept of convex analysis is provided and used to establish sufficient optimality conditions. We apply the theoretical results proven to the problem of the Brachistochrone.}, language = {en} }