Abstract:
An optimal control problem with linear dynamics is considered on a fixed time interval. The ends of the interval correspond to terminal spaces, and a finite-dimensional optimization problem is formulated on the Cartesian product of these spaces. Two components of the solution of this problem define the initial and terminal conditions for the controlled dynamics. The dynamics in the optimal control problem is treated as an equality constraint. The controls are assumed to be bounded in the norm of L2. A saddle-point method is proposed to solve the problem. The method is based on finding saddle points of the Lagrangian. The weak convergence of the method in controls and its strong convergence in state trajectories, conjugate trajectories, and terminal variables are proved.
Citation:
A. S. Antipin, E. V. Khoroshilova, “Optimal control with connected initial and terminal conditions”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 2, 2014, 13–28; Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), S9–S25
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\by A.~S.~Antipin, E.~V.~Khoroshilova
\paper Optimal control with connected initial and terminal conditions
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 2
\pages 13--28
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 289
\issue , suppl. 1
\pages S9--S25
\crossref{https://doi.org/10.1134/S0081543815050028}
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Linking options:
https://www.mathnet.ru/eng/timm1055
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This publication is cited in the following 16 articles:
Anatoly Antipin, Elena Khoroshilova, Lecture Notes in Computer Science, 13781, Optimization and Applications, 2022, 108
Anatoly Antipin, Elena Khoroshilova, Lecture Notes in Computer Science, 13078, Optimization and Applications, 2021, 151
A. S. Antipin, E. V. Khoroshilova, “Dynamics, phase constraints, and linear programming”, Comput. Math. Math. Phys., 60:2 (2020), 184–202
V. G. Malinov, “Projection generalized two-point extragradient quasi-Newton method for saddle-point and other problems”, Comput. Math. Math. Phys., 60:2 (2020), 227–239
A. Antipin, E. Khoroshilova, “Controlled dynamic model with boundary-value problem of minimizing a sensitivity function”, Optim. Lett., 13:3, SI (2019), 451–473
A. V. Fominykh, “Open-loop control of a plant described by a system with nonsmooth right-hand side”, Comput. Math. Math. Phys., 59:10 (2019), 1639–1648
A. S. Antipin, V. Jaćimović, M. Jaćimović, “Dynamics and variational inequalities”, Comput. Math. Math. Phys., 57:5 (2017), 784–801
A. Antipin, “Sufficient conditions and evidence-based solutions”, 2017 Constructive Nonsmooth Analysis and Related Topics (CNSA), Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 2017, 11–13
E. Khoroshilova, “Minimizing a sensitivity function as boundary-value problem in terminal control”, 2017 Constructive Nonsmooth Analysis and Related Topics (CNSA), Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 2017, 149–151
Anatoly Antipin, 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017, 1
Elena Khoroshilova, 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017, 1
A. Antipin, E. Khoroshilova, “Saddle point approach to solving problem of optimal control with fixed ends”, J. Glob. Optim., 65:1, SI (2016), 3–17
A. Antipin, E. Khoroshilova, “On methods of terminal control with boundary-value problems: Lagrange approach”, Optimization and Its Applications in Control and Data Sciences, In honor of Boris T. Polyak’s 80th birthday, Springer Optimization and Its Applications, 115, ed. B. Goldengorin, Springer, 2016, 17–49
A. S. Antipin, O. O. Vasilieva, “Dynamic method of multipliers in terminal control”, Comput. Math. Math. Phys., 55:5 (2015), 766–787
A. S. Antipin, E. V. Khoroshilova, “Mnogokriterialnaya kraevaya zadacha v dinamike”, Tr. IMM UrO RAN, 21, no. 3, 2015, 20–29
A. S. Antipin, E. V. Khoroshilova, “O kraevoi zadache terminalnogo upravleniya s kvadratichnym kriteriem kachestva”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 8 (2014), 7–28