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Mat. Sb., 1993, Volume 184, Number 6, Pages 3–32 (Mi msb991)  

This article is cited in 11 scientific papers (total in 11 papers)

First-order necessary conditions in the problem of optimal control of a differential inclusion with phase constraints

A. V. Arutyunov, S. M. Aseev, V. I. Blagodatskikh

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Nondegenerate first-order necessary conditions for optimality are obtained for the problem (1.1)–(1.4) under different assumptions about controllability at the endpoints. These necessary conditions are obtained in the Hamiltonian form of Clarke [1]. With the help of a smoothing technique [2] the perturbation method in [3] is used to carry the main results in [4] (there the case when the support function $H(x,t,\psi)=\sup_{y\in F(x,t)}\langle y,\psi\rangle$ depends smoothly on the variable $x$ is considered) over to the more natural class of problems with locally Lipschitz support function $H$.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 79:1, 117–139

Bibliographic databases:

UDC: 517.9
MSC: Primary 49K24, 49K15; Secondary 34A60
Received: 15.10.1992

Citation: A. V. Arutyunov, S. M. Aseev, V. I. Blagodatskikh, “First-order necessary conditions in the problem of optimal control of a differential inclusion with phase constraints”, Mat. Sb., 184:6 (1993), 3–32; Russian Acad. Sci. Sb. Math., 79:1 (1994), 117–139

Citation in format AMSBIB
\by A.~V.~Arutyunov, S.~M.~Aseev, V.~I.~Blagodatskikh
\paper First-order necessary conditions in the~problem of optimal control of a~differential inclusion with phase constraints
\jour Mat. Sb.
\yr 1993
\vol 184
\issue 6
\pages 3--32
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 79
\issue 1
\pages 117--139

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    This publication is cited in the following articles:
    1. Arutyunov A., Aseev S., “State Constraints in Optimal-Control - the Degeneracy Phenomenon”, Syst. Control Lett., 26:4 (1995), 267–273  crossref  mathscinet  zmath  isi
    2. Aram V. Arutyunov, Sergei M. Aseev, “Investigation of the Degeneracy Phenomenon of the Maximum Principle for Optimal Control Problems with State Constraints”, SIAM J Control Optim, 35:3 (1997), 930  crossref  mathscinet  zmath  isi  elib
    3. S. M. Aseev, “A method of smooth approximation in the theory of necessary optimality conditions for differential inclusions”, Izv. Math., 61:2 (1997), 235–258  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Franco Rampazzo, Richard Vinter, “Degenerate Optimal Control Problems with State Constraints”, SIAM J. Control Optim, 39:4 (2000), 989  crossref  mathscinet  zmath
    5. S. M. Aseev, “Extremal Problems for Differential Inclusions with State Constraints”, Proc. Steklov Inst. Math., 233 (2001), 1–63  mathnet  mathscinet  zmath
    6. S. M. Aseev, A. V. Kryazhimskii, A. M. Tarasyev, “The Pontryagin Maximum Principle and Transversality Conditions for an Optimal Control Problem with Infinite Time Interval”, Proc. Steklov Inst. Math., 233 (2001), 64–80  mathnet  mathscinet  zmath
    7. Bulcakov A.I., Grigorenko A.A., Korobko A.I., “On Approximation of the Perturbed Inclusion”, Georgian Math. J., 14:2 (2007), 253–267  mathscinet  isi
    8. A. I. Smirnov, “Necessary Optimality Conditions for a Class of Optimal Control Problems with Discontinuous Integrand”, Proc. Steklov Inst. Math., 262 (2008), 213–230  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    9. Zelikin M.I., Borisov V.F., “The Geometry of Extremals with Countably Many Contact Points with the Boundary of the Phase Constraint”, Dokl. Math., 81:1 (2010), 1–5  crossref  mathscinet  zmath  isi  elib
    10. M. I. Zelikin, V. V. Gael, “Accumulation of tangent points with the boundary and Lagrangian manifolds in problems with phase constraints”, J Math Sci, 177:2 (2011), 299  crossref  mathscinet  zmath
    11. V. F. Borisov, V. V. Gael, M. I. Zelikin, “Chattering regimes and Lagrangian manifolds in problems with phase constraints”, Izv. Math., 76:1 (2012), 1–38  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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