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Mat. Zametki, 2005, Volume 78, Issue 4, Pages 503–518 (Mi mz2609)  

This article is cited in 19 scientific papers (total in 19 papers)

Existence Theorem in the Optimal Control Problem on an Infinite Time Interval

A. V. Dmitruka, N. V. Kuz'kinab

a Central Economics and Mathematics Institute, RAS
b M. V. Lomonosov Moscow State University

Abstract: We consider the optimal control problem on an infinite time interval. The system is linear in the control, the functional is convex in the control, and the control set is convex and compact. We propose a new condition on the behavior of the functional at infinity, which is weaker than the previously known conditions, and prove the existence theorem for the solution under this condition. We consider several special cases and propose a general abstract scheme.

DOI: https://doi.org/10.4213/mzm2609

Full text: PDF file (264 kB)
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English version:
Mathematical Notes, 2005, 78:4, 466–480

Bibliographic databases:

UDC: 517.97
Received: 04.02.2004
Revised: 04.03.2005

Citation: A. V. Dmitruk, N. V. Kuz'kina, “Existence Theorem in the Optimal Control Problem on an Infinite Time Interval”, Mat. Zametki, 78:4 (2005), 503–518; Math. Notes, 78:4 (2005), 466–480

Citation in format AMSBIB
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    Erratum

    This publication is cited in the following articles:
    1. Zaslavski A. J., “Turnpike results for discrete-time optimal control systems arising in economic dynamics”, Nonlinear Anal., 67:7 (2007), 2024–2049  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    2. Zaslavski A. J., “A turnpike result for a class of problems of the calculus of variations with extended-valued integrands”, J. Convex Anal., 15:4 (2008), 869–890  mathscinet  zmath  isi  elib
    3. Pickenhain S., Lykina V., Wagner M., “On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems”, Control Cybernet., 37:2 (2008), 451–468  mathscinet  zmath  isi  elib
    4. Lykina V., “On a resource allocation model with infinite horizon”, Appl. Math. Comput., 204:2 (2008), 595–601  crossref  mathscinet  zmath  isi  elib  scopus
    5. Lykina V., Pickenhain S., Wagner M., “Different interpretations of the improper integral objective in an infinite horizon control problem”, J. Math. Anal. Appl., 340:1 (2008), 498–510  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Rudeva A.V., Shananin A.A., “Control synthesis in a modified Ramsey model with a liquidity constraint”, Differential Equations, 45:12 (2009), 1835–1839  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Zaslavski A.J., “Optimal solutions for a class of infinite horizon variational problems with extended-valued integrands”, Optimization, 59:2 (2010), 181–197  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. S. M. Aseev, K. O. Besov, A. V. Kryazhimskiy, “Infinite-horizon optimal control problems in economics”, Russian Math. Surveys, 67:2 (2012), 195–253  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. Pablo Rincon-Zapatero J., Santos M.S., “Differentiability of the Value Function in Continuous-Time Economic Models”, J. Math. Anal. Appl., 394:1 (2012), 305–323  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Khlopin D., “Necessity of Vanishing Shadow Price in Infinite Horizon Control Problems”, J. Dyn. Control Syst., 19:4 (2013), 519–552  crossref  mathscinet  zmath  isi  scopus  scopus
    11. A. N. Stanzhytskyi, E. A. Samoǐlenko, “Coefficient conditions for existence of an optimal control for systems of differential equations”, Siberian Math. J., 55:1 (2014), 156–170  mathnet  crossref  mathscinet  isi
    12. K. O. Besov, “On necessary optimality conditions for infinite-horizon economic growth problems with locally unbounded instantaneous utility function”, Proc. Steklov Inst. Math., 284 (2014), 50–80  mathnet  crossref  crossref  isi  elib  elib
    13. Khlopin D.V., “Necessity of Limiting Co-State Arcs in Bolza-Type Infinite Horizon Problem”, Optimization, 64:11 (2015), 2417–2440  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    14. S. M. Aseev, “Existence of an optimal control in infinite-horizon problems with unbounded set of control constraints”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 1–10  mathnet  crossref  crossref  mathscinet  isi  elib
    15. Lykina V., “An Existence Theorem for a Class of Infinite Horizon Optimal Control Problems”, J. Optim. Theory Appl., 169:1 (2016), 50–73  crossref  mathscinet  zmath  isi  elib  scopus
    16. Lykina V., Pickenhain S., “Budget-Constrained Infinite Horizon Optimal Control Problems With Linear Dynamics”, 2016 IEEE 55Th Conference on Decision and Control (Cdc), IEEE Conference on Decision and Control, IEEE, 2016, 1906–1911  isi
    17. Muthukumar P., Deepa R., “Infinite horizon optimal control of forward?backward stochastic system driven by Teugels martingales with Lévy processes”, Stoch. Dyn., 17:3 (2017), 1750020  crossref  mathscinet  zmath  isi  scopus
    18. Rokhlin D.B., Usov A., “Rational taxation in an open access fishery model”, Arch. Control Sci., 27:1 (2017), 5–27  crossref  mathscinet  isi
    19. K. O. Besov, “On Balder's Existence Theorem for Infinite-Horizon Optimal Control Problems”, Math. Notes, 103:2 (2018), 167–174  mathnet  crossref  crossref  mathscinet  isi  elib
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