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Mat. Sb. (N.S.), 1976, Volume 100(142), Number 4(8), Pages 610–643 (Mi msb3013)  

This article is cited in 27 scientific papers (total in 27 papers)

A second order optimality principle for a time-optimal problem

A. A. Agrachev, R. V. Gamkrelidze


Abstract: In this paper, a general necessary optimality condition of second order is proved for a time-optimal problem. Necessary optimality conditions of second order are applied, in general, in studying singular optimal regimes which can not be found with the aid of the first-order necessary condition for optimality, i.e. with the aid of the Pontryagin maximum principle.
Bibliography: 4 titles.

Full text: PDF file (2820 kB)
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English version:
Mathematics of the USSR-Sbornik, 1976, 29:4, 547–576

Bibliographic databases:

UDC: 519.3
MSC: 49B10
Received: 11.03.1976

Citation: A. A. Agrachev, R. V. Gamkrelidze, “A second order optimality principle for a time-optimal problem”, Mat. Sb. (N.S.), 100(142):4(8) (1976), 610–643; Math. USSR-Sb., 29:4 (1976), 547–576

Citation in format AMSBIB
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\by A.~A.~Agrachev, R.~V.~Gamkrelidze
\paper A~second order optimality principle for a~time-optimal problem
\jour Mat. Sb. (N.S.)
\yr 1976
\vol 100(142)
\issue 4(8)
\pages 610--643
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\transl
\jour Math. USSR-Sb.
\yr 1976
\vol 29
\issue 4
\pages 547--576
\crossref{https://doi.org/10.1070/SM1976v029n04ABEH003685}
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  • http://mi.mathnet.ru/eng/msb/v142/i4/p610

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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. A. Agrachev, “A second-order necessary condition for optimality in the general nonlinear case”, Math. USSR-Sb., 31:4 (1977), 493–506  mathnet  crossref  mathscinet  zmath  isi
    2. A. A. Agrachev, R. V. Gamkrelidze, “The exponential representation of flows and the chronological calculus”, Math. USSR-Sb., 35:6 (1979), 727–785  mathnet  crossref  mathscinet  zmath  isi
    3. E. S. Levitin, A. A. Milyutin, N. P. Osmolovskii, “Conditions of high order for a local minimum in problems with constraints”, Russian Math. Surveys, 33:6 (1978), 97–168  mathnet  crossref  mathscinet  zmath
    4. Gorokhovik V., “Necessary Conditions for 2nd-Order Optimization in Control-Problems with Vector-Valued Quality Indexes”, Differ. Equ., 19:10 (1983), 1238–1246  mathscinet  isi
    5. Gilbert E., Bernstein D., “2nd-Order Necessary Conditions in Optimal-Control - Accessory-Problem Results Without Normality Conditions”, J. Optim. Theory Appl., 41:1 (1983), 75–106  crossref  mathscinet  zmath  isi
    6. Gorokhovik V., “High-Order Necessary Optimality Conditions for Control-Problems with Terminal Constraints”, Optim. Control Appl. Methods, 4:2 (1983), 103–127  crossref  mathscinet  zmath  isi
    7. Dennis S. Bernstein, “A Systematic Approach to Higher-Order Necessary Conditions in Optimization Theory”, SIAM J Control Optim, 22:2 (1984), 211  crossref  mathscinet  zmath  isi
    8. Barbashina E., “Packet with Variable Control Variations .1.”, Differ. Equ., 20:8 (1984), 949–957  mathscinet  isi
    9. Barbashina E., “A Bundle with Variable Control Variations .2.”, Differ. Equ., 20:12 (1984), 1423–1430  mathscinet  isi
    10. Zelikin M., “The Theory of Linear-Control Problems”, 277, no. 4, 1984, 782–785  mathscinet  zmath  isi
    11. Agrachev A., Gamkrelidze R., “The Extremality Index and Quasi-Extremal Controls”, 284, no. 4, 1985, 777–781  mathscinet  zmath  isi
    12. A. I. Tret'yak, “On necessary conditions of arbitrary order for optimality in a time-optimal problem”, Math. USSR-Sb., 60:1 (1988), 255–268  mathnet  crossref  mathscinet  zmath
    13. Sarychev A., “High-Order Necessary Conditions of Optimality for Nonlinear Control-Systems”, Syst. Control Lett., 16:5 (1991), 369–378  crossref  mathscinet  zmath  isi
    14. Melikov T., “Recursive Conditions for Optimality of Singular Controls in Systems with Delay”, 322, no. 5, 1992, 843–846  mathscinet  zmath  isi
    15. Agrachev A. Sarychev A., “Abnormal Sub-Riemannian Geodesics: Morse Index and Rigidity”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 13:6 (1996), 635–690  crossref  mathscinet  zmath  isi
    16. Agrachev A., Sigalotti M., “On the Local Structure of Optimal Trajectories in R-3”, SIAM J. Control Optim., 42:2 (2003), 513–531  crossref  mathscinet  zmath  isi
    17. M. Sigalotti, “Regularity properties of optimal trajectories of single-input control systems in dimension three”, Journal of Mathematical Sciences (New York), 126:6 (2005), 1561  crossref  mathscinet  zmath
    18. Sigalotti M., “Local Regularity of Optimal Trajectories for Control Problems with General Boundary Conditions”, J. Dyn. Control Syst., 11:1 (2005), 91–123  crossref  mathscinet  zmath  isi  elib
    19. V. F. Borisov, “Kelley Condition and Structure of Lagrange Manifold in a Neighborhood of a First-Order Singular Extremal”, Journal of Mathematical Sciences, 151:6 (2008), 3431–3472  mathnet  crossref  mathscinet  zmath  elib
    20. Bonnard B., Caillau J.-B., Trelat E., “Second Order Optimality Conditions in the Smooth Case and Applications in Optimal Control”, ESAIM-Control OPtim. Calc. Var., 13:2 (2007), 207–236  crossref  mathscinet  zmath  isi
    21. M. I. Zelikin, L. V. Lokutsievskiy, R. Hildebrand, “Geometry of neighborhoods of singular trajectories in problems with multidimensional control”, Proc. Steklov Inst. Math., 277 (2012), 67–83  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    22. Tan K., Yang X., “Subriemannian Geodesics of Carnot Groups of Step 3”, ESAIM-Control OPtim. Calc. Var., 19:1 (2013), 274–287  crossref  mathscinet  zmath  isi
    23. Frankowska H., Tonon D., “Pointwise Second-Order Necessary Optimality Conditions for the Mayer Problem with Control Constraints”, SIAM J. Control Optim., 51:5 (2013), 3814–3843  crossref  mathscinet  zmath  isi
    24. Mansimov K.B., Mardanov M.J., “Necessary Conditions of the Optimality of the Second Order in Optimal Control Problems Described by the System of Integrodifferential Equations of the Volterra Type”, J. Automat. Inf. Sci., 45:8 (2013), 59–67  crossref  isi
    25. L. V. Lokutsievskii, “The Hamiltonian property of the flow of singular trajectories”, Sb. Math., 205:3 (2014), 432–458  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    26. M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand, “Typicality of chaotic fractal behavior of integral vortices in Hamiltonian systems with discontinuous right hand side”, Journal of Mathematical Sciences, 221:1 (2017), 1–136  mathnet  crossref
    27. M. D. Mardanov, T. K. Melikov, “On the theory of singular optimal controls in dynamic systems with control delay”, Comput. Math. Math. Phys., 57:5 (2017), 749–769  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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