@book{Pickenhain, author = {Pickenhain, Sabine}, title = {On adequate transversality conditions for infinite horizon optimal control problems}, publisher = {Cottbus : BTU, Math. Inst.}, language = {en} } @incollection{Pickenhain, author = {Pickenhain, Sabine}, title = {Hilbert space treatment of optimal control problems with infinite horizon}, series = {Modeling, Simulation and Optimization of Complex Processes - HPSC 2012}, booktitle = {Modeling, Simulation and Optimization of Complex Processes - HPSC 2012}, publisher = {Springer-Verlag}, address = {Heidelberg [u.a.]}, isbn = {978-3-319-09062-7}, doi = {10.1007/978-3-319-09063-4}, pages = {169 -- 182}, language = {en} } @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} } @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} } @misc{PickenhainBurtchenKoloetal., author = {Pickenhain, Sabine and Burtchen, Angie and Kolo, Katharina and Lykina, Valeriya}, title = {An indirect pseudospectral method for the solution of linear-quadratic optimal control problems with infinite horizon}, series = {Optimization}, volume = {65}, journal = {Optimization}, number = {3}, issn = {0233-1934}, doi = {10.1080/02331934.2015.1014481}, pages = {609 -- 633}, 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} } @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} } @misc{PickenhainLykina, author = {Pickenhain, Sabine and Lykina, Valeriya}, title = {Weighted functional spaces approach in infinite horizon optimal control problems: A systematic analysis of hidden opportunities and advantages}, series = {Journal of Mathematical Analysis and Applications}, volume = {454}, journal = {Journal of Mathematical Analysis and Applications}, number = {1}, issn = {0022-247X}, pages = {195 -- 218}, language = {en} } @misc{PickenhainLykina, author = {Pickenhain, Sabine and Lykina, Valeriya}, title = {Pontryagin Type Maximum Principle for budget-constrained infinite horizon optimal control problems with linear dynamics}, series = {Journal of Mathematical Analysis and Applications}, volume = {457}, journal = {Journal of Mathematical Analysis and Applications}, number = {2}, issn = {0022-247X}, pages = {1591 -- 1612}, language = {en} } @incollection{PickenhainBurtchen, author = {Pickenhain, Sabine and Burtchen, Angie}, title = {Optimal Energy Control of Hybrid Vehicles}, series = {Modeling, Simulation and Optimization of Complex Processes HPSC 2015}, booktitle = {Modeling, Simulation and Optimization of Complex Processes HPSC 2015}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-67167-3}, doi = {10.1007/978-3-319-67168-0_15}, pages = {179 -- 188}, abstract = {In recent years route planning has been greatly facilitated by car navigation systems. The desire for resource-efficient traveling has increased, a fact that is reflected by a higher demand for hybrid vehicles. The combination of electric motor and combustion engine adapted to the specific driving situation clearly reduces fuel consumption in comparison to vehicles with a conventional combustion engine. Up to this point, despite the fact that energy consumption and travel time are significantly affected by the drivers individual driving style, the driver has mainly been excluded. The aim of this project is to develop a dynamic model to calculate the optimal power train control—including the route planning. Taking into account the maximum travel time of the entire travel route in combination with energy-minimized driving, this approach allows us to obtain a new powerful concept. We present the model and its formulation as an optimal control problem, as well as some numerical results.}, language = {en} }