Skip to main content
Log in

On payload insertion to the given point

  • Applications of Mathematical Programming
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Consideration was given to the problem of optimal program control of the launcher vehicle of the “Soyuz-2” class for insertion the maximal mass to the given neighborhood of a point on the near-earth elliptical orbit, as well as the problem of estimating the set of reachable orbit points. Two kinds of numerical algorithms were developed and realized. The results of numerical modeling and, in particular, determination of the points by two methods were presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Krasovskii, N.N., Teoriya upravleniya dvizheniem (Motion Control Theory), Moscow: Nauka, 1968.

    Google Scholar 

  2. Mazgalin, D.V. and Pochinskii, V.I., Method of Determining the Launch Azimuth and the Pitch Angle Program at the Active Atmospheric Segment of the LV Flight, Vestn. YuUrGU, “Computer Technologies, Control, and Radioelectronics,” 2010, vol. 12, no. 22(198), pp. 47–50.

  3. Mazgalin, D.V., Designing Technique to Control the Launcher Vehicle at using the Program Angular Speeds of Turn as Controls, Informats.-Upravlyayushch. Sist., 2010, no. 3(46), pp. 21–29.

  4. Appazov, R.F. and Sytin, O.G., Metody proektirovaniya traektorii nositelei i sputnikov Zemli (Methods of Designing the Trajectories of Carriers and Earth Satellites), Moscow: Nauka, 1987.

    Google Scholar 

  5. Bryson, A.E., Jr. and Ho Yu-Chi, Applied Optimal Control: Optimization, Estimation, and Control, Waltham: Blaisdell, 1969. Translated under the title Prikladnaya teoriya optimal’nogo upravleniya, Moscow: Mir, 1972.

    Google Scholar 

  6. Fedorenko, R.P., Priblizhennoe reshenie zadach optimal’nogo upravleniya (Approximate Solution of the Optimal Control Problems), Moscow: Nauka, 1978.

    MATH  Google Scholar 

  7. Kurzhanskii, A.B., Upravlenie i nablyudenie v usloviyakh neopredelennosti (Control and Observation under Uncertainty), Moscow: Nauka, 1977.

    MATH  Google Scholar 

  8. Kurzhanski, A.B. and Vályi, I., Ellipsoidal Calculus for Estimation and Control, Boston: Birkhäuser, 1997.

    MATH  Google Scholar 

  9. Chernous’ko, F.L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem. Metod ellipsoidov (Estimation of the Phase State of Dynamic Systems. Method of Ellipsoids) Moscow: Nauka, 1988.

    MATH  Google Scholar 

  10. Gusev, M.I., Estimates of the Reachability Sets of the Multidimensional Controlled Systems with Nonlinear Cross-connections, Tr. Inst. Mat. Mekh. UrO RAN, 2009, vol. 15, no. 4, pp. 82–94.

    Google Scholar 

  11. Filippova, T.F., Estimates of Trajectory Tubes of Uncertain Nonlinear Control Systems, in Lecture Notes Comput. Sci., 2010, vol. 5910, pp. 272–279.

    Article  Google Scholar 

  12. Panasyuk, A.I. and Panasyuk, V.I., Asimptoticheskaya magistral’naya optimizatsiya upravlyaemykh sistem (Asymptotic Magistral Optimization of the Controlled Systems), Minsk: Nauka i Tekhnika, 1986.

    Google Scholar 

  13. Kostousova, E.K., Parallelotope-based External and Internal Estimation of the Reachability Domains, Vychisl. Tekhnol., 1998, vol. 3, no. 2, pp. 11–20.

    MathSciNet  MATH  Google Scholar 

  14. Dumsheva, T.D., Kostousov, V.B., Kostousova, E.K., and Pochinskii, V.I., Studying the Problem of Optimal Payload Insertion to the Given Elliptical Orbit, Tr. Inst. Mat. Mekh. UrO RAN, 2010, vol. 16, no. 5, pp. 57–65.

    Google Scholar 

  15. Polyak, B.T., Method of Conjugate Gradients in the Extremum Problems, Zh. Vychisl. Mat. Mat. Fiz., 1969, vol. 9, no. 4, pp. 807–821.

    MATH  Google Scholar 

  16. Orlov, V.S., Polyak, B.T., Rebrii, V.A., and Tret’yakov, N.V., Experience in Solving the Optimal Control Problems, in Sb. “Vychislitel’nye metody and programmirovanie” (Collected Papers “Computational Methods and Programming”), Moscow: Mosk. Gos. Univ., 1967, vol. 9, pp. 179–192.

    Google Scholar 

  17. Kostousova, E.K. and Pochinskii, V.I., On Problems Inserting Launcher Vehicles to the Given Elliptical Orbits, Tr. Inst. Mat. Mekh. UrO RAN, 2011, vol. 17, no. 3, pp. 201–216.

    Google Scholar 

  18. Okhotsimskii, D.E and Sikharulidze, Yu.G., Osnovy mekhaniki kosmicheskogo poleta (Fundamentals of the Space Flight Mechanics), Moscow: Nauka, 1990.

    Google Scholar 

  19. Lyubushin, A.A. and Chernous’ko, F.L., Method of Successive Approximations for Calculation of the Optimal Control, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1983, no. 2, pp. 147–159.

  20. Parallel Computations at the Ural Branch, Russian Academy of Sciences. Sections “Computing Resources,” “Cluster Software: Parallel Matlab,” http://wwwrus.imm.uran.ru/C9/Parallel/.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © T.D. Dumsheva, V.B. Kostousov, E.K. Kostousova, V.I. Pochinskii, 2012, published in Avtomatika i Telemekhanika, 2012, No. 4, pp. 18–31.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dumsheva, T.D., Kostousov, V.B., Kostousova, E.K. et al. On payload insertion to the given point. Autom Remote Control 73, 616–625 (2012). https://doi.org/10.1134/S0005117912040029

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117912040029

Keywords

Navigation