TY - JOUR A1 - Malanowski, Kazimierz A1 - Maurer, Helmut A1 - Pickenhain, Sabine T1 - Second-order sufficient conditions for state-constrained optimal control problems Y1 - 2004 ER - TY - JOUR A1 - Pickenhain, Sabine A1 - Wagner, M. T1 - Pontryagin principle for state-constrained control problems governed by a first-order PDE system Y1 - 2000 ER - TY - CHAP A1 - Pickenhain, Sabine A1 - Wagner, M. ED - Ioffe, Alexander T1 - Critical points in relaxed deposit problems T2 - 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 Y1 - 2000 SN - 0-8493-0605-1 SP - 217 EP - 236 PB - Chapman & Hall/CRC CY - Boca Raton, Fla. [u.a.] ER - TY - JOUR A1 - Maurer, Helmut A1 - Pickenhain, Sabine T1 - Second-order sufficient conditions for control problems with mixed control-state constraints Y1 - 1995 ER - TY - CHAP A1 - Pickenhain, Sabine A1 - Klötzler, R. ED - Bulirsch, Roland T1 - Pontryagin's maximum principle for multidimensional control problems T2 - Optimal control, Conference on Optimal Control, held at the Mathematisches Forschungsinstitut of the University of Freiburg Y1 - 1993 SN - 0-8176-2887-8 SP - 21 EP - 30 PB - Birkhäuser CY - Basel [u.a.] ER - TY - JOUR A1 - Pickenhain, Sabine A1 - Wagner, Marcus T1 - Piecewise Continuous Controls in Dieudonné-Rashevsky Type Problems Y1 - 2005 ER - TY - CHAP A1 - Pickenhain, Sabine A1 - Malanowski, Kazimierz A1 - Maurer, Helmut ED - Cagnol, John T1 - Second order sufficient conditions for optimal control subject to first order state constraints T2 - Control and boundary analysis Y1 - 2005 SN - 978-1-574-44594-7 SP - 293 EP - 304 PB - Chapman & Hall/CRC CY - Boca Raton, Fla ER - TY - CHAP A1 - Pickenhain, Sabine A1 - Lykina, Valeriya T1 - Sufficiency conditions for infinite horizon optimal control problems Y1 - 2006 ER - TY - JOUR A1 - Pickenhain, Sabine A1 - Wagner, Marcus T1 - Minimizing sequences in class-qualified deposit problems Y1 - 2006 ER - TY - CHAP A1 - Pickenhain, Sabine T1 - On infinite horizon optimal control of a Lotka-Voltera-System T2 - Recent Advances in Optimization and its Applications in Engineering : The 14th Belgian-French-German Conference on Optimization Y1 - 2010 SN - 978-3-642-12598-0 SP - 277 EP - 286 PB - Springer CY - Berlin [u.a.] ER - TY - JOUR A1 - Pickenhain, Sabine T1 - Duality theory for state-constrained control problems governed by a first order PDE system JF - Control and Cybernetics Y1 - 2002 VL - 31 IS - 3 SP - 833 EP - 845 ER - TY - CHAP A1 - Pickenhain, Sabine A1 - Wagner, M. ED - Grötschel, Martin T1 - Optimal Control Problems with a First Order PDE System - Necessary and Sufficient Optimality Conditions T2 - Online optimization of large scale systems Y1 - 2001 SN - 3-540-42459-8 SP - 159 EP - 172 PB - Springer CY - Berlin [u.a.] ER - TY - CHAP A1 - Pickenhain, Sabine ED - Floudas, Christodoulos A. ED - Pardalos, Panos M. T1 - Duality in optimal control with first order differential equations T2 - Encyclopedia of optimization, Bd. 1 Y1 - 2001 SN - 0-7923-7029-5 SP - 472 EP - 477 PB - Kluwer CY - Dordrecht [u.a.] 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 - CHAP A1 - Pickenhain, Sabine ED - Deweß, Günter T1 - Wälzlagerrollen - Löcher - Orbiformen T2 - Heureka heute : Kostproben praxiswirksamer Mathematik Y1 - 1993 SN - 3-8154-2071-7 SN - 3-7281-2029-4 SP - 122 EP - 133 PB - Teubner CY - Stuttgart [u.a.] ER - TY - GEN A1 - Pickenhain, Sabine A1 - Burtchen, Angie T1 - Regulator Problems on Unbounded Domains : Stationarity–Optimal Control–Asymptotic Controllability T2 - Vietnam Journal of Mathematics N2 - 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. KW - Weighted functional spaces KW - Optimal control KW - Asymptotic controllability KW - Infinite horizon Y1 - 2018 U6 - https://doi.org/10.1007/s10013-018-0304-0 SN - 2305-2228 VL - 46 IS - 4 SP - 837 EP - 861 ER - TY - RPRT A1 - Pickenhain, Sabine A1 - Lykina, Valeriya T1 - Pontryagin Type Maximum Principle for Budget-Constrained Infinite Horizon Optimal Control Problems with Linear Dynamics N2 - 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. KW - budget constraint KW - infinite horizon KW - Pontryagin Type Maximum Principle KW - weighted Sobolev spaces KW - linear-quadratic regulator KW - optimal control Y1 - 2017 PB - Brandenburgische Technische Universität, Mathematisches Institut CY - Cottbus-Senftenberg 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 - RPRT A1 - Pickenhain, Sabine T1 - Infinite Horizon Problems in the Calculus of Variations - The Role of Transformations with an Application to the Brachistochrone Problem N2 - 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. KW - weighted functional spaces KW - calculus of variations KW - infinite horizon Y1 - 2017 PB - Brandenburgische Technische Universität, Mathematisches Institut CY - Cottbus ; Senftenberg 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 - GEN A1 - Pickenhain, Sabine A1 - Ziemann, Torsten T1 - First-order necessary optimality conditions for infinite horizon optimal control problems with linear dynamics and convex objective T2 - Optimization : a Journal of Mathematical Programming and Operations Research N2 - We consider a class of infinite horizon optimal control problems with vector-valued states and controls involving the Lebesgue integral in the objective and a linear dynamics. The key idea is to show that the solutions of the state-equation belong to a weighted Hilbert space, due to a natural growth condition. This allows to introduce the weighted Sobolev space as the state space and the weighted Lebesgue space as the control space in the problem setting. We answer the fundamental question of how one can choose the weight function in dependence of the system dynamics. In the setting of Hilbert spaces, we show a Pontryagin-type maximum principle. Therefore, we use techniques from earlier publications of the authors. In contrast to these publications, we deal with vector-valued states and controls, here. These vector-valued problems arise in many applications. The maximum principle also includes a transversality condition which makes the difference to related publications in the field of necessary optimality conditions. This condition brings advantages for the numerical calculations of the solution by indirect methods, like a pseudospectral method. KW - vector-valued optimal control KW - infinite horizon KW - necessary optimality conditions Y1 - 2018 U6 - https://doi.org/10.1080/02331934.2018.1434172 SN - 1029-4945 SN - 0233-1934 VL - 67 IS - 6 SP - 757 EP - 782 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 - 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 - GEN A1 - Pickenhain, Sabine A1 - Burtchen, Angie T1 - Problems in the Calculus of Variations on Unbounded Intervals—Fourier–Laguerre Analysis and Approximations T2 - Vietnam Journal of Mathematics N2 - In this paper, we consider a class of variational problems on an unbounded interval of the real axis. This type of problems arises, e.g., in quantum mechanics and asymptotic controllability. The problem is treated in a Hilbert space setting with uniformly and non-uniformly weighted Sobolev spaces as state spaces. We provide sufficient conditions that a function from a weighted Sobolev space can be expanded into a Fourier–Laguerre series converging together with its distributional derivative pointwisely and uniformly. With this result, the considered variational problem is transformed into a problem in the sequence space of Fourier–Laguerre coefficients. We develop a Fourier–Laguerre method in these spaces in order to construct a polynomial approximation scheme for the solution of this problem. Y1 - 2019 U6 - https://doi.org/10.1007/s10013-019-00349-3 SN - 2305-221X SN - 2305-2228 VL - 47 IS - 3 SP - 617 EP - 638 ER - TY - GEN A1 - Pickenhain, Sabine T1 - Infinite Horizon Problems in the Calculus of Variations. The Role of Transformations with an Application to the Brachistochrone Problem T2 - Set-Valued and Variational Analysis Theory and Applications N2 - 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. KW - weighted functional spaces KW - calculus of variations KW - infinite horizon Y1 - 2019 U6 - https://doi.org/10.1007/s11228-018-0483-6 SN - 1877-0541 VL - 27 IS - 2 SP - 331 EP - 354 ER - TY - CHAP A1 - Pickenhain, Sabine T1 - On adequate transversality conditions for infinite horizon optimal control problems Y1 - 2010 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 - 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 - 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 - BOOK A1 - Pickenhain, Sabine T1 - On adequate transversality conditions for infinite horizon optimal control problems Y1 - 2009 PB - Cottbus : BTU, Math. Inst. ER - TY - JOUR A1 - Lykina, Valeriya A1 - Pickenhain, Sabine A1 - Wagner, M. T1 - Different interpretations of the improper integral objective in an infinite horizon control problem Y1 - 2008 ER - TY - CHAP A1 - Pickenhain, Sabine T1 - Rough stability of solutions to nonconvex optimization problems Y1 - 2000 ER - TY - GEN A1 - Pickenhain, Sabine A1 - Lykina, Valeriya A1 - Wagner, Markus T1 - On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems T2 - Control and Cybernetics Y1 - 2008 SN - 0324-8569 VL - 37 SP - 451 EP - 468 ER - TY - JOUR A1 - Lykina, Valeriya A1 - Pickenhain, Sabine A1 - Wagner, M. T1 - On a resource allocation model with inifinite horizon Y1 - 2008 ER - TY - JOUR A1 - Pickenhain, Sabine T1 - A pointwise maximum principle in optimal control with multiple integrals Y1 - 1996 ER - TY - JOUR A1 - Pickenhain, Sabine A1 - Kripfganz, A. T1 - In celebration of Prof. Dr. Rolf Klötzler 65th birthday Y1 - 1996 ER -