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 Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 2, Pages 13–28 (Mi timm1055)

Optimal control with connected initial and terminal conditions

A. S. Antipina, E. V. Khoroshilovab

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

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 $\mathrm L_2$. 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.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 289, suppl. 1, S9–S25

Bibliographic databases:

UDC: 517.977

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

This publication is cited in the following articles:
1. 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
2. A. S. Antipin, O. O. Vasilieva, “Dynamic method of multipliers in terminal control”, Comput. Math. Math. Phys., 55:5 (2015), 766–787
3. A. S. Antipin, E. V. Khoroshilova, “Mnogokriterialnaya kraevaya zadacha v dinamike”, Tr. IMM UrO RAN, 21, no. 3, 2015, 20–29
4. 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
5. 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
6. A. S. Antipin, V. Jaćimović, M. Jaćimović, “Dynamics and variational inequalities”, Comput. Math. Math. Phys., 57:5 (2017), 784–801
7. 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
8. 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
9. Antipin A. Khoroshilova E., “Controlled Dynamic Model With Boundary-Value Problem of Minimizing a Sensitivity Function”, Optim. Lett., 13:3, SI (2019), 451–473
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