TY - BOOK A1 - Pickenhain, Sabine T1 - On adequate transversality conditions for infinite horizon optimal control problems Y1 - 2009 PB - Cottbus : BTU, Math. Inst. ER - TY - CHAP A1 - Pickenhain, Sabine T1 - Hilbert space treatment of optimal control problems with infinite horizon T2 - Modeling, Simulation and Optimization of Complex Processes - HPSC 2012 Y1 - 2014 SN - 978-3-319-09062-7 U6 - https://doi.org/10.1007/978-3-319-09063-4 SP - 169 EP - 182 PB - Springer-Verlag CY - Heidelberg [u.a.] ER - TY - CHAP A1 - Wenzke, Diana A1 - Lykina, Valeriya A1 - Pickenhain, Sabine T1 - State and Time Transformations of Infinite Horizon Optimal Control Problems T2 - Variational and Optimal Control Problems on Unbounded Domains (AMS) Y1 - 2014 SN - 978-1-4704-1077-3 SN - 978-1-4704-1713-0 SP - 189 EP - 208 PB - American Mathematical Society (AMS) CY - Providence, RI ER - TY - GEN A1 - Pickenhain, Sabine T1 - Infinite Horizon Optimal Control Problems in the Light of Convex Analysis in Hilbert Spaces T2 - Set-Valued and Variational Analysis N2 - 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. KW - Infinite horizon KW - Optimal control KW - Pontryagin’s Maximum Principle Y1 - 2015 U6 - https://doi.org/10.1007/s11228-014-0304-5 SN - 1877-0533 SN - 1877-0541 VL - 23 IS - 1 SP - 169 EP - 189 ER - TY - GEN A1 - Pickenhain, Sabine A1 - Burtchen, Angie A1 - Kolo, Katharina A1 - Lykina, Valeriya T1 - An indirect pseudospectral method for the solution of linear-quadratic optimal control problems with infinite horizon T2 - Optimization KW - optimal control KW - linear-quadratic problem KW - weighted Lebesgue spaces Y1 - 2015 U6 - https://doi.org/10.1080/02331934.2015.1014481 SN - 0233-1934 SN - 1029-4945 VL - 65 IS - 3 SP - 609 EP - 633 ER - TY - RPRT A1 - Wenzke, Diana A1 - Pickenhain, Sabine T1 - Transformation of Infinite Horizon Optimal Control Problems N2 - 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. Y1 - 2012 PB - Mathematisches Institut CY - Cottbus ER - TY - CHAP A1 - Pickenhain, Sabine A1 - Lykina, Valeriya T1 - Budget-Constrained Infinite horizon Optimal Control Problems with Linear Dynamics T2 - 55th IEEE Conference on Decision and Control, Las Vegas Y1 - 2016 SN - 978-1-5090-1837-6 SN - 978-1-5090-1838-3 U6 - https://doi.org/10.1109/CDC.2016.7798543 SP - 1906 EP - 1911 PB - IEEE CY - Piscataway, NJ ER - TY - CHAP A1 - Burtchen, Angie A1 - Pickenhain, Sabine A1 - Maurer, Helmut T1 - Numerical Treatment of the Optimal Energy Control Problem of Hybrid Vehicles T2 - IEEE 55th Conference on Decision and Control (CDC], December 12-14, 2016, Las Vegas Y1 - 2016 SN - 978-1-5090-1837-6 U6 - https://doi.org/10.1109/CDC.2016.7799409 SP - 7377 EP - 7383 ER - TY - GEN A1 - Pickenhain, Sabine A1 - Lykina, Valeriya T1 - Weighted functional spaces approach in infinite horizon optimal control problems: A systematic analysis of hidden opportunities and advantages T2 - Journal of Mathematical Analysis and Applications Y1 - 2017 UR - http://www.sciencedirect.com/science/article/pii/S0022247X17304328?via%3Dihub SN - 0022-247X VL - 454 IS - 1 SP - 195 EP - 218 ER - TY - GEN A1 - Pickenhain, Sabine A1 - Lykina, Valeriya T1 - Pontryagin Type Maximum Principle for budget-constrained infinite horizon optimal control problems with linear dynamics T2 - Journal of Mathematical Analysis and Applications Y1 - 2017 UR - http://www.sciencedirect.com/science/article/pii/S0022247X17307503?via%3Dihub SN - 0022-247X VL - 457 IS - 2 SP - 1591 EP - 1612 ER - TY - CHAP A1 - Pickenhain, Sabine A1 - Burtchen, Angie T1 - Optimal Energy Control of Hybrid Vehicles T2 - Modeling, Simulation and Optimization of Complex Processes HPSC 2015 N2 - 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. Y1 - 2017 SN - 978-3-319-67167-3 SN - 978-3-319-67168-0 U6 - https://doi.org/10.1007/978-3-319-67168-0_15 SP - 179 EP - 188 PB - Springer CY - Cham ER -