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Mat. Sb. (N.S.), 1978, Volume 107(149), Number 4(12), Pages 541–571 (Mi msb2694)  

This article is cited in 40 scientific papers (total in 42 papers)

Differential games. Approximation and formal models

N. N. Krasovskii


Abstract: Certain control problems under conditions of undetermined information for systems described by differential equations can be formalized within the framework of differential games. The present paper is devoted to one such formalization developed by the author and his collaborators.
Bibliography: 22 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:6, 795–822

Bibliographic databases:

UDC: 518.9
MSC: Primary 90D25; Secondary 93C15
Received: 06.09.1978

Citation: N. N. Krasovskii, “Differential games. Approximation and formal models”, Mat. Sb. (N.S.), 107(149):4(12) (1978), 541–571; Math. USSR-Sb., 35:6 (1979), 795–822

Citation in format AMSBIB
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\by N.~N.~Krasovskii
\paper Differential games. Approximation and formal models
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 107(149)
\issue 4(12)
\pages 541--571
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\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 6
\pages 795--822
\crossref{https://doi.org/10.1070/SM1979v035n06ABEH001625}
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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. Krasovskii A., “A Non-Linear Differential Game with Value Given by an Integral”, Differ. Equ., 18:8 (1982), 911–916  mathscinet  isi
    2. Subbotina N., “Universal Optimal Strategies in Positional Differential-Games”, Differ. Equ., 19:11 (1983), 1377–1382  mathnet  mathscinet  zmath  isi
    3. Baibazarov M. Subbotin A., “Determination of the Value of a Differential Game”, Differ. Equ., 20:9 (1984), 1068–1073  mathscinet  isi
    4. Dzhafarov V., “The Stability of Guaranteed Result in the Problem of Feedback-Control”, 285, no. 1, 1985, 27–31  mathscinet  zmath  isi
    5. Serkov D., “Synthesis of the Feedback-Control for a Parabolic-System and Stochastic Maximin”, 283, no. 3, 1985, 553–559  mathscinet  zmath  isi
    6. Pashkov A., Terekhov S., “A Differential Game of Approach with 2 Pursuers and One Evader”, J. Optim. Theory Appl., 55:2 (1987), 303–311  crossref  mathscinet  zmath  isi
    7. Maksimov V., “Positional Modeling of Controls and Initial Functions for Volterra Systems”, Differ. Equ., 23:4 (1987), 418–426  mathnet  mathscinet  isi
    8. Levchenkov A., Pashkov A., “Differential Game of Optimal Approach of 2 Inertial Pursuers to a Noninertial Evader”, J. Optim. Theory Appl., 65:3 (1990), 501–518  crossref  mathscinet  zmath  isi
    9. Brykalov S., “The Existence of Temperature Distributions Close to a Prescribed One in Some Control-Systems”, 19, no. 4, 1990, 279–288  mathscinet  zmath  isi
    10. Baibazarov M., Ushakov V., “Existence of a Value of Differential-Games with Integral Constraints”, Differ. Equ., 27:6 (1991), 648–656  mathnet  mathscinet  isi
    11. Garnysheva G., Subbotin A., “Strategies of Minimax Aiming in the Direction of the Quasi-Gradient”, Pmm-J. Appl. Math. Mech., 58:4 (1994), 575–581  crossref  mathscinet  zmath  isi
    12. Clarke P.H., Ledyaev Yu.S., Stern R.J., Wolenski P.R., “Qualitative properties of trajectories of control systems: A survey”, J. Dynam. Control Systems, 1:1 (1995), 1–48  crossref  mathscinet  zmath  elib
    13. Garnysheva G., Subbotin A., “Suboptimal Universal Strategies in an Optimum-Time Game Problem”, Pmm-J. Appl. Math. Mech., 59:5 (1995), 677–683  crossref  mathscinet  zmath  isi
    14. A. I. Subbotin, “Minimax solutions of first-order partial differential equations”, Russian Math. Surveys, 51:2 (1996), 283–313  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. F. Clarke, Yu. S. Ledyaev, A. I. Subbotin, “Universal Feedback Control via Proximal Aiming in Problems of Control under Disturbance and Differential Games”, Proc. Steklov Inst. Math., 224 (1999), 149–168  mathnet  mathscinet  zmath
    16. Brykalov S., “A Scalar Conflict Control Problem with Nonlinear Functional Condition”, Nonsmooth and Discontinuous Problems of Control and Optimization (NDPCO'98), eds. Batukhtin V., Kirillova F., Ukhobotov V., Elsevier Science BV, 1999, 95–97  mathscinet  isi
    17. Brykalov S., “Continuous Feedback in Problems of Conflict Control”, Dokl. Math., 63:1 (2001), 59–61  mathscinet  zmath  isi
    18. Brykalov S., “Continuous Strategies in Differential Games”, Differ. Equ., 38:4 (2002), 471–477  mathnet  crossref  mathscinet  zmath  isi
    19. Brykalov S., “Conflict-Control Systems and Differential Inclusions”, Differ. Equ., 38:3 (2002), 310–316  mathnet  crossref  mathscinet  zmath  isi
    20. Clarke F., Rifford L., Stern R., “Feedback in State Constrained Optimal Control”, ESAIM-Control OPtim. Calc. Var., 7:5 (2002), 97–133  crossref  mathscinet  zmath  isi
    21. Brykalov S., “Two Evasion Problems in a Plane with Separate Controls and Non-Convex Terminal Sets”, Pmm-J. Appl. Math. Mech., 67:2 (2003), 167–173  crossref  mathscinet  zmath  isi
    22. V. I. Berdyshev, A. B. Kurzhanskii, E. F. Mishchenko, Yu. S. Osipov, V. V. Rumyantsev, “Nikolai Nikolaevich Krasovskii (on the occasion of his 80th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 2004no. , suppl. 2, S1–S19  mathnet  mathscinet  zmath  elib
    23. Brykalov S., “On Differential Games with Undetermined Initial Vectors”, Dokl. Math., 69:3 (2004), 416–418  zmath  isi
    24. Patsko V., “Switching Surfaces in Linear Differential Games with a Fixed Instant of Termination”, Pmm-J. Appl. Math. Mech., 68:4 (2004), 583–595  crossref  mathscinet  zmath  isi
    25. Brykalov S., “Continuous Single-Valued Strategies in Evasion Problems”, Pmm-J. Appl. Math. Mech., 68:4 (2004), 575–582  crossref  mathscinet  zmath  isi
    26. Brykalov S., “Multivalued Feedback with the Semicontinuity Property”, Differ. Equ., 41:8 (2005), 1080–1086  mathnet  crossref  mathscinet  zmath  isi  elib
    27. Brykalov S.A., “Continuous Strategies in Differential Games with Nonconvex Target Sets”, Dokl. Math., 73:2 (2006), 207–209  crossref  mathscinet  zmath  isi  elib
    28. D. A. Serkov, “Ctrategii minimaksnogo riska (sozhaleniya) v sisteme s prostymi dvizheniyami”, Tr. IMM UrO RAN, 13, no. 3, 2007, 121–135  mathnet  elib
    29. S. A. Brykalov, Ya. A. Latushkin, “On continuous strategies of deviation from a nonconvex set under uncertainty conditions”, Autom. Remote Control, 68:11 (2007), 2002–2014  mathnet  crossref  mathscinet  zmath  elib  elib
    30. Brykalov S.A., “Continuous Feedback Control in Evasion Problems with Nonconvex Target Set”, Differ. Equ., 43:5 (2007), 605–612  crossref  mathscinet  zmath  isi  elib
    31. Ancona F., Bressan A., “Nearly Time Optimal Stabilizing Patchy Feedbacks”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 24:2 (2007), 279–310  crossref  mathscinet  zmath  adsnasa  isi
    32. A. G. Chentsov, “Quasistrategies in an abstract guidance control problem”, Russian Math. (Iz. VUZ), 52:10 (2008), 46–59  mathnet  crossref  mathscinet  zmath  elib
    33. V. I. Berdyshev, S. V. Emel'yanov, A. B. Kurzhanskii, E. F. Mishchenko, Yu. S. Osipov, “Nikolai Nikolaevich Krasovskii (on the occasion of his 85th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S1–S14  mathnet  crossref  isi  elib
    34. N. N. Krasovskii, A. N. Kotel'nikova, “An approach-evasion differential game: Stochastic guide”, Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S191–S213  mathnet  crossref  elib
    35. Krasovskii N.N., Kotel'nikova A.N., “Unification of differential games, generalized solutions of the Hamilton–Jacobi equations, and a stochastic guide”, Differ. Equ., 45:11 (2009), 1653–1668  crossref  mathscinet  zmath  isi  elib  elib
    36. N. N. Krasovskii, A. N. Kotel'nikova, “On a differential interception game”, Proc. Steklov Inst. Math., 268 (2010), 161–206  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    37. N. Yu. Lukoyanov, “On Hamilton–Jacobi formalism in time-delay control systems”, Tr. IMM UrO RAN, 16, no. 5, 2010, 269–277  mathnet  elib
    38. N. N. Krasovskii, A. N. Kotelnikova, “O differentsialnoi igre na perekhvat”, Tr. IMM UrO RAN, 16, no. 5, 2010, 113–126  mathnet
    39. Brykalov S.A., “Razreshimost kraevykh zadach s nepreryvnoi obratnoi svyazyu”, Doklady akademii nauk, 442:4 (2012), 439–439  zmath  elib
    40. Brykalov S.A., “Solvability of Boundary Value Problems with Continuous Feedback”, Dokl. Math., 85:1 (2012), 68–70  crossref  mathscinet  zmath  isi  elib
    41. V. A. Dykhta, “Weakly monotone solutions of the Hamilton–Jacobi inequality and optimality conditions with positional controls”, Autom. Remote Control, 75:5 (2014), 829–844  mathnet  crossref  isi
    42. “Nikolai Nikolaevich Krasovskii (on the occasion of his 90th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 1–21  mathnet  crossref  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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