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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 4, Pages 29–37 (Mi timm1112)  
This article is cited in 8 scientific papers (total in 8 papers)

Conditions for the absence of jumps of the solution to the adjoint system of the maximum principle for optimal control problems with state constraints

A. V. Arutyunova, D. Yu. Karamzinb, F. L. Pereirac

a Peoples Friendship University of Russia
b Dorodnitsyn Computing Centre of the Russian Academy of Sciences
c University of Porto, Portugal
Full-text PDF (179 kB) Citations (8)
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Abstract: Properties of Lagrange multipliers from the Pontryagin maximum principle for problems with state constraints are investigated. Sufficient conditions for the continuity of the solution of the adjoint solution depending on how the extremal trajectory approaches the state constraint boundary are obtained. The proof uses the notion of closure by measure of a Lebesgue measurable function and the Caratheodory theorem.
Keywords: optimal control, maximum principle, state constraints.
Received: 10.07.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 292, Issue 1, Pages 27–35
DOI: https://doi.org/10.1134/S0081543816020036
Bibliographic databases:
Document Type: Article
UDC: 517.977.52
Language: Russian
Citation: A. V. Arutyunov, D. Yu. Karamzin, F. L. Pereira, “Conditions for the absence of jumps of the solution to the adjoint system of the maximum principle for optimal control problems with state constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 4, 2014, 29–37; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 27–35
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/timm/v20/i4/p29
    • This publication is cited in the following 8 articles:
    1. Boris Miller, Evgeny Rubinovich, Systems & Control: Foundations & Applications, Optimization of Dynamical Systems with Impulse Controls and Shocks, 2024, 257  crossref
    2. N. I. Pogodaev, M. V. Staritsyn, “Exact formulae for the increment of the objective functional and necessary optimality conditions, alternative to Pontryagin's maximum principle”, Sb. Math., 215:6 (2024), 790–822  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Aram Arutyunov, Dmitry Karamzin, “A Survey on Regularity Conditions for State-Constrained Optimal Control Problems and the Non-degenerate Maximum Principle”, J Optim Theory Appl, 184:3 (2020), 697  crossref
    4. Aram Arutyunov, Dmitry Karamzin, Fernando Lobo Pereira, Lecture Notes in Control and Information Sciences, 477, Optimal Impulsive Control, 2019, 99  crossref
    5. A. Arutyunov, D. Karamzin, F. L. Pereira, “A remark on the continuity of the measure Lagrange multiplier in state constrained optimal control problems”, 2018 IEEE Conference on Decision and Control (CDC), IEEE, 2018, 49–54  crossref  isi
    6. A. Dmitruk, I. Samylovskiy, “On the relation between two approaches to necessary optimality conditions in problems with state constraints”, J. Optim. Theory Appl., 173:2 (2017), 391–420  crossref  mathscinet  zmath  isi  scopus
    7. Dmitry Karamzin, Valeriano de Oliveira, Fernando Pereira, Geraldo Silva, “Minimax optimal control problem with state constraints”, European Journal of Control, 32 (2016), 24  crossref
    8. A. V. Arutyunov, D. Yu. Karamzin, “On some continuity properties of the measure Lagrange multiplier from the maximum principle for state constrained problems”, SIAM J. Control Optim., 53:4 (2015), 2514–2540  crossref  mathscinet  zmath  isi  scopus
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