TY - CHAP A1 - Pickenhain, Sabine A1 - Lykina, Valeriya T1 - Sufficiency conditions for infinite horizon optimal control problems Y1 - 2006 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 - Lykina, Valeriya T1 - Existence Theorem for Infinite Horizon Optimal Control Problems with Mixed Control-State Isoperimetrical Constraint T2 - Large-Scale Scientific Computing, 11th International Conference, LSSC 2017, Sozopol, Bulgaria, June 5-9, 2017 N2 - In this paper a class of infinite horizon optimal control problems with a mixed control-state isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamics is allowed. The problem setting includes a weighted Sobolev space as the state space. For this class of problems, we establish an existence theorem. The proved theoretical result is applied to a mixed control-state budget constrained advertisement model. KW - infinite horizon KW - existence theorem KW - weighted sobolev spaces Y1 - 2018 SN - 978-3-319-73440-8 SN - 978-3-319-73441-5 U6 - https://doi.org/10.1007%2F978-3-319-73441-5_24 SP - 228 EP - 236 PB - Springer CY - Cham ER - TY - RPRT A1 - Mehicic-Eberhardt, Sana A1 - Schrape, Stefanie A1 - Krause, Lars A1 - Vadachkoriya, Sofiya A1 - Lebedynska, Yuliya A1 - Möller, Sarah A1 - Lykina, Valeriya ED - Woll, Ralf ED - Albrecht, Eike ED - Mißler-Behr, Magdalena ED - Hoppe, Annette ED - Berger, Ulrich ED - Kalusche, Wolfdietrich ED - Pickenhain, Sabine T1 - Risikodefinition aus verschiedenen Anwendungssichten - Diskussionspapier der Fachklasse "Modelle, Methoden und Werkzeuge zum Risikomanagement" der International Graduate School der BTU Cottbus Y1 - 2008 PB - BTU, UWV Eigenverlag CY - Cottbus ER - TY - THES A1 - Lykina, Valeriya T1 - Beiträge zur Theorie der Optimalsteuerungsprobleme mit unendlichem Zeithorizont Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:co1-opus-18615 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 - Lykina, Valeriya T1 - An Existence Theorem for a Class of Infinite Horizon Optimal Control Problems T2 - Journal of Optimization Theory and Applications N2 - In this paper, we deal with infinite horizon optimal control problems involving affine-linear dynamics and prove the existence of optimal solutions. The innovation of this paper lies in the special setting of the problem, precisely in the choice of weighted Sobolev and weighted Lebesgue spaces as the state and control spaces, respectively, which turns out to be meaningful for various problems. We apply the generalized Weierstraß theorem to prove the existence result. A lower semicontinuity theorem which is needed for that is shown under weakened assumptions. KW - Existence theorem KW - Weighted Sobolev and Lebesgue spaces KW - Weak lower semicontinuity Y1 - 2016 U6 - https://doi.org/10.1007/s10957-013-0500-8 SN - 0022-3239 SN - 1573-2878 VL - 169 IS - 1 SP - 50 EP - 73 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 - 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 - Lykina, Valeriya A1 - Grass, Dieter T1 - Infinite horizon cancer treatment model with isoperimetrical constraint: existence of optimal solutions and numerical analysis T2 - International Journal of Control N2 - In this paper, a class of infinite horizon optimal control problems with a mixed control-state isoperimetrical constraint, also interpreted as a budget constraint, is considered. The underlying dynamics is assumed to be affine-linear in control. The crucial idea which is followed in this paper is the choice of a weighted Sobolev space as the state space. For this class of problems, we establish an existence result and apply it to a bilinear model of optimal cancer treatment with an isoperimetrical constraint including the overall amount of drugs used during the whole therapy horizon. A numerical analysis of this model is provided by means of open source software package OCMat, which implements a continuation method for solving discounted infinite horizon optimal control problems. KW - infinite horizon optimal control KW - existence theorem KW - weighted sobolev spaces KW - numerical solution Y1 - 2019 U6 - https://doi.org/10.1080/00207179.2017.1396362 SN - 1366-5820 SN - 0020-7179 VL - 92 IS - 6 SP - 1401 EP - 1414 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 - 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 - 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 -