Skip to main content
SpringerLink
Log in

On the nonlinear uniaxial reorientation problem for a three-rotor gyrostat in the game noise model

  • Nonlinear Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We solve a nonlinear game problem of uniaxial reorientation for an asymmetric solid body with three flywheels (rotors). We give an estimate for admissible levels of uncontrollable noise depending on given constraints on controlling moments.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pyatnitskii, E.S., Decomposition Principle in Controlling Mechanical Systems, Dokl. Akad. Nauk SSSR, 1988, vol. 300, no. 2, pp. 300–303.

    MathSciNet  Google Scholar 

  2. Chernous’ko, F.L., Decomposition and Suboptimal Control in Dynamical Systems, Prikl. Mat. Mekh., 1990, vol. 54, no. 6, pp. 883–893.

    MathSciNet  Google Scholar 

  3. Chernous’ko, F.L., Decomposition and Control Synthesis in Dynamical Systems, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1990, no. 6, pp. 64–82.

  4. Siljak, D.D., Decentralized Control of Complex Systems, Cambridge: Academic, 1991.

    Google Scholar 

  5. Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear Adaptive Control for Complex Dynamical Systems), St. Petersburg: Nauka, 2000.

    Google Scholar 

  6. Chernous’ko, F.L., Anan’evskii, I.M., and Reshmin, S.A., Metody upravleniya nelineinymi mekhanicheskimi sistemami (Control Methods for Nonlinear Mechanical Systems), Moscow: Fizmatlit, 2006.

    Google Scholar 

  7. Matyukhin, V.I., Upravlenie mekhanicheskimi sistemami (Control in Mechanical Systems), Moscow: Fizmatlit, 2009.

    Google Scholar 

  8. Reshmin, S.A., Decomposition Method in the Control Problem of Lagrange System with a Deficit of Controlling Parameters, Prikl. Mat. Mekh., 2010, vol. 74, no. 1, pp. 151–169.

    MathSciNet  Google Scholar 

  9. Aleksandrov, A.Yu. and Kosov, A.A., On Stability and Stabilization of Nonlinear Nonstationary Mechanical Systems, Prikl. Mat. Mekh., 2010, vol. 74, no. 5, pp. 774–788.

    Google Scholar 

  10. Vorotnikov, V.I., On Nonlinear Synthesis of Bounded Controls with Noise, Dokl. Ross. Akad. Nauk, 1994, vol. 337, no. 1, pp. 44–47.

    MathSciNet  Google Scholar 

  11. Vorotnikov, V.I., On Constructing Game Bounded Controls for Nonlinear Dynamical Systems, Prikl. Mat. Mekh., 1997, vol. 61, no. 1, pp. 63–74.

    MathSciNet  Google Scholar 

  12. Vorotnikov, V.I., Partial Stability and Control, Boston: Birkhauser, 1998.

    MATH  Google Scholar 

  13. Vorotnikov, V.I. and Rumyantsev, V.V., Ustoichivost’ i upravlenie po chasti koordinat fazovogo vektora dinamicheskikh sistem: teoriya, metody i prilozheniya (Stability and Control for a Part of Phase Vector Coordinates in Dynamical Systems), Moscow: Nauchnyi Mir, 2001.

    Google Scholar 

  14. Zubov, V.I., Lektsii po teorii upravleniya (Lectures in Control Theory), Moscow: Nauka, 1975.

    MATH  Google Scholar 

  15. Filippov, A.F., Differentsial’nye uravneniya s razryvnoi pravoi chast’yu (Differential Equations with a Discontinuous Right-Hand Side), Moscow: Nauka, 1985.

    Google Scholar 

  16. Krasovskii, N.N., Igrovye zadachi o vstreche dvizhenii (Game Problems on Meeting Motions), Moscow: Nauka, 1970.

    Google Scholar 

  17. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1983.

    MATH  Google Scholar 

  18. Vorotnikov, V.I. and Martyshenko, Yu.G., On Partial Detectability of Nonlinear Dynamic Systems, Autom. Remote Control, 2009, vol. 70, no. 1, pp. 20–32.

    Article  MathSciNet  MATH  Google Scholar 

  19. Gulyaev, V.P., Koshkin, V.L., and Savilova, I.V., Time-Optimal Control for a Three-Axial Orientation of a Solid Body with Constrained Control Parameters, Izv. Akad. Nauk SSSR, Mekh. Tverdogo Tela, 1986, no. 5, pp. 11–15.

  20. Vorotnikov, V.I., Ustoichivost’ dinamicheskikh sistem po otnosheniyu k chasti peremennykh (Partial Stability of Dynamic Systems), Moscow: Nauka, 1991.

    Google Scholar 

  21. Vorotnikov, V.I., Optimal Stabilization of Nonlinear Systems, Autom. Remote Control, 1991, vol. 52, no. 3, pp. 314–324.

    MathSciNet  MATH  Google Scholar 

  22. Vorotnikov, V.I. and Martyshenko, Yu.G., On the Nonlinear Game Problem of Uniaxial Asymmetric Solid Body, Sist. Upravlen. Inf. Tekhnol., 2010, no. 2(40), pp. 4–8.

  23. Vorotnikov, V.I., Partial Stability and Control: The State-of-the-Art and Development Prospects, Autom. Remote Control, 2005, vol. 66, no. 4, pp. 511–561.

    Article  MathSciNet  MATH  Google Scholar 

  24. Vorotnikov, V.I., On Controlling the Rotation of a Solid Body. Game-Theoretic Approach, Prikl. Mat. Mekh., 1994, vol. 58, no. 3, pp. 82–103.

    MathSciNet  Google Scholar 

  25. Ermoshina, O.V. and Krishchenko, A.P., Synthesis of Program Controls for Space Vehicle Orientation with the Inverse Dynamics Problem Method, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2000, no. 2, pp. 155–162.

  26. Bai, X. and Junkins, J.L., New Results for Time-Optimal Three-Axis Reorientation of a Rigid Spacecraft, J. Guidance, Control, Dynam., 2009, vol. 22, no. 4, pp. 1071–1076.

    Article  Google Scholar 

  27. Alekseev, K.B., Malyavin, A.A., and Shchadyan, A.V., Extensive Control for the Orientation of a Space Vehicles Based on Fuzzy Logic, Polet, 2009, no. 1, pp. 47–53.

  28. Bedrossian, N.S., Bhatt, S., Kang, W., et al., Zero Propellant Maneuver Guidance, IEEE Control Syst. Mag., 2009, vol. 29, no. 1, pp. 53–73.

    Article  MathSciNet  Google Scholar 

  29. Emel’yanov, S.V. and Korovin, S.K., Novye tipy obratnoi svyazi. Upravlenie pri neopredelennosti (New Types of Feedback: Control under Uncertainty), Moscow: Fizmatlit, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ural State Technical University, Nizhni Tagil Technological Institute, Nizhni Tagil, Russia

    V. I. Vorotnikov & Yu. G. Martyshenko

Authors
  1. V. I. Vorotnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. G. Martyshenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.I. Vorotnikov, Yu.G. Martyshenko, 2012, published in Avtomatika i Telemekhanika, 2012, No. 9, pp. 35–48.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vorotnikov, V.I., Martyshenko, Y.G. On the nonlinear uniaxial reorientation problem for a three-rotor gyrostat in the game noise model. Autom Remote Control 73, 1469–1480 (2012). https://doi.org/10.1134/S0005117912090032

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117912090032

Keywords

Search

Navigation