Professor Dr. Vadim Krotov

Institute of Control Sciences, 
Russian Academy of Sciences, Moscow




December, 1998


1967 Full Professor Diploma (Speciality: Flight Dynamics and Control), Moscow Aviation Institute, Moscow.

1963 Doctor of Sciences (equal to German Habilitation) in Engineering (Speciality: Flight Dynamics and Control), Moscow Aviation Institute, Moscow.

1962 Ph. D. in Phys. & Math. (Speciality: Differential equations), Steklovís Mathematic Institute, USSR Academy of Sciences, Moscow.

1958-61 Postgraduate course (Speciality: Theoretical Mechanics), Baumanís High Technical School, Moscow.

1956 M.Sc. in Engineering, Mosow State Baumanís Technical University (MVTU), Moscow.

Professional Experience

1982- till recently: Head of Optimal Control Laboratory, Institute of Control Sciences, Russian Academy of Sciences, Moscow.

1982-1996: Professor, Cybernetics Dept., Institute of Economics & Statistics, Moscow.

1974-1982: Professor, Head of Cybernetics Department, Institute of Economics & Statistics, Moscow.

1972-1974: Head of Mathematics Department, Institute of Planning & Control, Moscow.

1969-1972: Professor, Head of the High Mathematics Dept., Institute of Aviation Technology, Moscow.

1961-69: Full Professor, Associate Professor, Research Fellow. Department of Flight Dynamics and Control, Moscow Aviation Institute; Moscow.


Research Interests and Activities:

  1. Theory of nonlinear controlled dynamic systems with emphasis to optimal control theory (and calculus of variations), icluding the systems, described by ordinary differential equations, part differential equations, multistage dynamic equations (with discrete time), systems with incomplete information.

  2. Basic results, which had been obtained and are developed:
    a) New classes of the solutions of variational problems (discontinuous solutions, sliding regimes).
    b) New sufficient conditions for global optimality of the control and the methods solving control problems based on this.
    c) Applied control problems for automatic control, optimal trajectories of the aircraft and spacecraft, modern problems of applied physics (for example, laser radiation action to a matter for the energy inflation, synthesis of new matters and other).
  3. Variational principles and analysis of some theoretical physics foundations.

  4. a) New relativistic theory of elastic continuum, new effects and analogies with electrodynamics and quantum mechanics. Relation to the unified geometric theories of field.
    b) Some consequences from observation theory related to quantum theory. Geometrodynamic models of the quantum phenomenon.

Professional Societies Membership:

Editorial Activities:


Gagarinís Medal "For participation in the fulfillment of USSR Space Program", 1984.

List of 15 Most Significant Publications:

  1. Krotov V.F. Basic problem of the variational calculus for functionals on the set of discontinuous functions. Doklady of the USSR Acad. Nauk, 1961, N1, v. 137. (*)
  2. Krotov V.F. Methods of solution of variational problems on the basis of sufficient conditions for absolute minimum. I,II,III. Avtomatika i Telemekhanika (Transl. as "Automation and Remote Control"), 23(1962) N12; 24(1963),N5; 25(1964), N7. (*)
  3. Krotov V.F., Bukreev V.Z. and Gurman V.I. New Variational Methods in Flight Dynamics. (Monograph). Mashinostroyenie Publ., Moscow, 1969. (English transl. by National Aeronaut. & Space Adm. (NASA), Transl. TTF-657, 1971, USA).
  4. Krotov V.F. & Gurman V.I. Methods and Problems of Optimal Control (Monograph). Moscow, Nauka Publ., 1973 (in Russian).
  5. Krotov V.F. Computing methods for solution and optimization of the controlled systems of equations I, II. Izvestia of USSR Acad. Nauk, Ser. Techn. Cybern. N5, N6, 1975. (*)
  6. Krotov V.F. Space-Time Elasticity and Foundations of Electrodynamics and Gravitation Theory. Journal of Franklin Inst., 1987, v. 323, p. 345-372, N.-Y.
  7. Krotov V.F Technique of Global Bounds in Optimal Control Theory. Control and Cybernetics (Journal of Polish Academy of Sc.), v.17 (1988), N 2,3.
  8. Krotov V.F Global methods to improve control and optimal control of resonance interaction of light and matter. Modelling and Control of Systems. Proceedings of the Bellman Continuum Workshop 1988. Springer-V. Berlin, N.Y., Paris.
  9. Krotov V.F. Observation of linear systems and principles of quantum mechanics. Doklady USSR Acad. Nauk, v.316, N1,1991. (*)
  10. Krotov V.F. & Lagosha B.A. Basis of optimal control theory (University textbook). Moscow, High School Publ., 1990 (in Russian).
  11. Krotov V.F. Relativistic Elasticity. Izvestia of Russian Acad. Nauk, Ser. Mechanics of Solid, N 6, 1992. (*)
  12. Krotov V.F. Elastic closure of general theory of relativity. Doklady Acad. Nauk, v.333, p.727-729. 1993. (*)
  13. Vadim F.Krotov. Global Methods in Optimal Control Theory (Monograph). Marcel Dekker Ink., Series of Monographs and Textbooks in Pure and Applied Mathematics. New-York, Basel, Hong Kong, 1996, 408p.
  14. Krotov V.F. Optimal control of flight trajectories. I,II.Avtomatika i Telemekhanika. N2, 1996; N2, 1997). (*)
  15. Krotov V.F. About principles of quantum mechanics. Doklady Acad. Nauk, v.353, N6 (April), 1997. (*)
(*) These Journals are translated into English.

Personal Data:

Full name: Krotov Vadim Fedorovitch

Born: January 14, 1932, Khabarovsk, Russia
Nationality: Russian
Civil status: married, 2 children

Office address: Institute of Control Sciences, Russian Academy of Sciences,
65 Profsoyuznaya, Moscow, 117806, Russia
Telefax: +7095 420-20-16
Telephone: +7095 334-91-59 (tel/faxmodem)

Home address: 11-2-156 , Artamonova street, Moscow,121357, Russia
Home telephone:  +7095 445-42-09

Last updated: December 7, 1998