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Mat. Sb. (N.S.), 1978, Volume 107(149), Number 4(12), Pages 467–532 (Mi msb2692)  

This article is cited in 57 scientific papers (total in 57 papers)

The exponential representation of flows and the chronological calculus

A. A. Agrachev, R. V. Gamkrelidze


Abstract: In this article is developed a calculus which reflects the most general group-theoretic properties of flows and which is based on an exponential representation of flows defined by nonstationary differential equations. Problems of optimization and control have had the greatest influence on the development of this calculus, and the results are intended mainly to treat these problems.
Bibliography: 11 titles.

Full text: PDF file (4979 kB)
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English version:
Mathematics of the USSR-Sbornik, 1979, 35:6, 727–785

Bibliographic databases:

UDC: 517.938+517.317
MSC: 34H05, 49B10, 93B05
Received: 30.08.1978

Citation: A. A. Agrachev, R. V. Gamkrelidze, “The exponential representation of flows and the chronological calculus”, Mat. Sb. (N.S.), 107(149):4(12) (1978), 467–532; Math. USSR-Sb., 35:6 (1979), 727–785

Citation in format AMSBIB
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\by A.~A.~Agrachev, R.~V.~Gamkrelidze
\paper The exponential representation of flows and the chronological calculus
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 107(149)
\issue 4(12)
\pages 467--532
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=524203}
\zmath{https://zbmath.org/?q=an:0429.34044|0408.34044}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 6
\pages 727--785
\crossref{https://doi.org/10.1070/SM1979v035n06ABEH001623}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

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    2. A. V. Sarychev, “The index of the second variation of a control system”, Math. USSR-Sb., 41:3 (1982), 383–401  mathnet  crossref  mathscinet  zmath
    3. A. A. Agrachev, A. V. Sarychev, “On reduction of a smooth system linear in the control”, Math. USSR-Sb., 58:1 (1987), 15–30  mathnet  crossref  mathscinet  zmath
    4. A. A. Agrachev, S. A. Vakhrameev, “Linearly controlled systems of constant rank and relay conditions for extreme control”, Russian Math. Surveys, 41:6 (1986), 199–200  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. M. V. Karasev, “Analogues of the objects of Lie group theory for nonlinear Poisson brackets”, Math. USSR-Izv., 28:3 (1987), 497–527  mathnet  crossref  mathscinet  zmath
    6. H. J. Sussmann, “A General Theorem on Local Controllability”, SIAM J Control Optim, 25:1 (1987), 158  crossref  mathscinet  zmath  isi
    7. 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
    8. Agrachev A., Sarychev A., “Filtrations of the Vector Field Lie-Algebras and Nilpotent Approximation for Control-Systems”, 295, no. 4, 1987, 777–781  mathscinet  zmath  isi
    9. Agrachev A., Gamkrelidze R., Sarychev A., “Local Invariants of Smooth Control-Systems”, Acta Appl. Math., 14:3 (1989), 191–237  crossref  mathscinet  zmath  isi
    10. A. I. Tret'yak, “On necessary conditions for odd optimability of high speed prbblem for the linear on control systems”, Math. USSR-Sb., 70:1 (1991), 47–63  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. Agrachev A., Gamkrelidze R., “The Time Substitution Variation in Optimal-Control”, 311, no. 2, 1990, 265–270  mathscinet  isi
    12. Tretyak A., “On Necessary Conditions of Even-Order Optimality in the Time-Optimization Problem for One Class of Control-Systems”, 316, no. 5, 1991, 1058–1060  mathscinet  zmath  isi
    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. Agrachev A., Gamkrelidze R., “Local-Controllability and Semigroups of Diffeomorphisms”, Acta Appl. Math., 32:1 (1993), 1–57  crossref  mathscinet  zmath  isi
    15. S. A. Vakhrameev, “A theorem on the finiteness of the switching number for smooth non-linear controlled systems”, Russian Math. Surveys, 49:6 (1994), 218–220  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. Montgomery R., “Singular Extremals on Lie-Groups”, Math. Control Signal Syst., 7:3 (1994), 217–234  crossref  mathscinet  zmath  isi
    17. S. A. Vakhrameev, “An existence theorem for a non-linear time-optimal problem in a class of bang-bang controls with finitely many switchings”, Russian Math. Surveys, 51:2 (1996), 353–354  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
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    19. Andrei V. Sarychev, “First- and Second-Order Sufficient Optimality Conditions for Bang-Bang Controls”, SIAM J Control Optim, 35:1 (1997), 315  crossref  mathscinet  zmath  isi
    20. Komleva T., “Sufficient Condition of Completion of a Pursuit in a Nonlinear Differential Game”, Cybern. Syst. Anal., 35:6 (1999), 960–964  crossref  mathscinet  zmath  isi
    21. Sklyar G., Ignatovich S., “Moment Approach to Nonlinear Time Optimality”, SIAM J. Control Optim., 38:6 (2000), 1707–1728  crossref  mathscinet  zmath  isi
    22. Francesco Bullo, “Series Expansions for the Evolution of Mechanical Control Systems”, SIAM J Control Optim, 40:1 (2001), 166  crossref  mathscinet  zmath  isi
    23. Mikhail Krastanov, Marc Quincampoix, “Local small time controllability and attainability of a set for nonlinear control system”, ESAIM: COCV, 6 (2001), 499  crossref  mathscinet  zmath
    24. Sarychev A., “Lie- and Chronologico-Algebraic Tools for Studying Stability of Time-Varying Systems”, Syst. Control Lett., 43:1 (2001), 59–76  crossref  mathscinet  zmath  isi
    25. Hirschorn R., Lewis A., “Geometric First-Order Controllability Conditions for Affine Connection Control Systems”, Proceedings of the 40th IEEE Conference on Decision and Control, Vols 1-5, IEEE Conference on Decision and Control, IEEE, 2001, 4216–4221  crossref  isi
    26. J. Cortes, S. Martinez, F. Bullo, “On nonlinear controllability and series expansions for Lagrangian systems with dissipative forces”, IEEE Trans Automat Contr, 47:8 (2002), 1396  crossref  mathscinet  zmath  isi
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    28. A. V. Selin, “A method for approximate analysis of a linear evolutionary equation in a Hilbert space”, Comput. Math. Math. Phys., 42:7 (2002), 901–914  mathnet  mathscinet  zmath  elib
    29. Korobov V., Skoryk V., “Synthesis of Restricted Inertial Controls for Systems with Multivariate Control”, J. Math. Anal. Appl., 275:1 (2002), 84–107  crossref  mathscinet  zmath  isi
    30. Stefanovski J., Trencevski K., “Analytic Solutions of Systems”, J. Dyn. Control Syst., 8:4 (2002), 463–486  crossref  mathscinet  zmath  isi
    31. Korobov V., Skorik V., “Positional Synthesis of Bounded Inertial Controls for Systems with One-Dimensional Control”, Differ. Equ., 38:3 (2002), 332–348  mathnet  crossref  mathscinet  zmath  isi
    32. Sarychev A., “Higher-Order Techniques for Some Problems of Nonlinear Control”, Math. Probl. Eng., 8:4-5 (2002), 413–438  crossref  mathscinet  zmath  isi
    33. Chelouah A., Chitour Y., “On the Motion Planning of Rolling Surfaces”, Forum Math., 15:5 (2003), 727–758  crossref  mathscinet  zmath  isi
    34. Kirov N., Krastanov M., “Higher Order Approximations of Affinely Controlled Nonlinear Systems”, Large-Sale Scientific Computing, Lecture Notes in Computer Science, 2907, eds. Lirkov I., Margenov S., Wasniewski J., Yalamov P., Springer-Verlag Berlin, 2003, 230–237  crossref  mathscinet  isi
    35. Rocha E., “On Computation of the Logarithm of the Chen-Fliess Series for Nonlinear Systems”, Nonlinear and Adaptive Control, Ncn4 2001, Lecture Notes in Control and Information Sciences, 281, eds. Zinober A., Owens D., Springer-Verlag Berlin, 2003, 317–326  crossref  mathscinet  zmath  isi
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    38. 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
    39. Kirov N., Krastanov M., “Volterra Series and Numerical Approximations of ODEs”, Numerical Analysis and its Applications, Lecture Notes in Computer Science, 3401, eds. Li Z., Vulkov L., Wasniewski J., Springer-Verlag Berlin, 2005, 337–344  crossref  mathscinet  zmath  adsnasa  isi
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  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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