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

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 2, Pages 13–28 (Mi timm1055)

This article is cited in 16 scientific papers (total in 16 papers)

Optimal control with connected initial and terminal conditions

A. S. Antipin^a, E. V. Khoroshilova^b

^a Dorodnitsyn Computing Centre of the Russian Academy of Sciences
^b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Full-text PDF (229 kB) Citations (16)

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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

L_{2}

$\mathrm L_2$ . 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.

Keywords: terminal control, boundary value problems, convex programming, Lagrange function, solution methods, convergence.

Received: 19.01.2014

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 289, Issue 1, Pages S9–S25
DOI: https://doi.org/10.1134/S0081543815050028

Bibliographic databases:

Document Type: Article

UDC: 517.977

Language: Russian

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

Citation in format AMSBIB

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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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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